•••••••••I 


THE  LIBRARY 

OF 
THE  UNIVERSITY 

OF  CALIFORNIA 
LOS  ANGELES 

GIFT 


PRIMARY  METHODS 

V 

A  COMPLETE   AND  METHODICAL   PRESENTATION 

OF  THE  USE   OF  KINDERGARTEN  MATERIAL 

IN  THE  WORK  OF  THE  PRIMARY  SCHOOL 


UNFOLDING 


A  Systematic  Course  of  Manual  Training  in  Connection  with  Arithmetic, 
Geometry,  Drawing,  and  other  School-Studies 


BY 


W.    N.    HAILMANN,    A.M. 

SUPERINTENDENT  OF  PUBLIC  SCHOOLS,  LA  PORTE,  INDIANA 


COPYRIGHT,  1887 

A.     S.     BARNES    &    COMPANY 

NEW   YORK    AND   CHICAGO 


Education 
Library 

L-B 

t  /&< 


TO    THE    TRUSTEES 

OF  THB 

LA  PORTE  PUBLIC  SCHOOLS 

AND  TO  THE  GOOD  PEOPLE  OF  LA  PORTE,  TO  WHOSE  SYMPATHETIC  AID  THE 
AUTHOR  OWES  SO  MUCH,  THIS  VOLUME  IS  GRATEFULLY  INSCRIBED. 


086094 


J^ffl&^i&C^Uh^^^ 


The  growing-  demand  among  primary 
teachers  for  "busy  work,"  "kindergarten 
methods,"  and  other  means  of  manual  occu- 
pation, has  led  to  the  preparation  of  this 
little  Arolume. 

Its  suggestions  have  grown  in  the  school- 
room, and  are  the  results  of  careful  expe- 
rience and  of  a  thoughtful  study  of  the 
children's  needs,  as  well  as  of  the  drift  and 
value  of  manual  work  as  an  educational 
factor.  In  this  work  I  have  "been  much 
aided  "by  the  teachers  of  the  Primary  Schools 
of  La  Porte,  who,  with  rare  intelligence, 
singleness  of  purpose,  and  professional  devo- 
tion; have  enabled  me  to  work  out  the 
"bearings  and  possibilities  of  the  work  in 
the  various  branches  of  school  instruction 
involved.  Whatever  credit,  therefore,  may 


vi  PREFACE. 

come  to  tlie  book,  is   largely   due   to   their 
ready  zeal. 

It  is  hoped  tliat  this  book  will  not  only 
supply  teachers  with  the  needed  means  and 
directions  for  the  methodical  and  system- 
atic, the  economical  and  efficient  use  of 
the  occupations  described,  but  "will  also 
successfully  guard  them  against  the  evils 
of  random  "busy  work." 

W.  N.  HAILMANN. 
LA  PORTE,  IND.,  July,  1887. 


CHAPTER 

I. — THINGS  BEFORE  WORDS  IN  EXPRESSION 


PAGE 
1 


II. — THE  COURSE  OF  STUDY 7 

III. — GIFTS  AND  OCCUPATIONS     .      „..«..     13 
IV. — THE  WORK  SELECTED — OUTFIT  .....        19 

V. — SECOND-GIFT  BEADS .23 

VI. — SECOND-GIFT  BEADS 33 

VII. — A  NUMERAL  FRAME  FOR  EACH  PUPIL       ...     45 

VIII. — COUNTING  BLOCKS 53 

IX. — COUNTING  BLOCKS        .      .......     65 

X. — FOLDING  SHEET 73 

XL — FOLDING  SHEET     .      .      . 83 

XIL— PLASTIC  CLAY 93 

XIII. — CUTTING  AND  MOUNTING 101 

XrV. — CARD-BOARD 'WORK 113 

XV. — FRACTION  STRIPS 121 

XVL— SPLINTS  OR  STICKS 129 

XVII.— STICKS  AND  PEAS        .      .      .      .      .      .      .      .139 

XVIII. — LENTILS  OR  DOTS 147 

XIX.— THE  GROUP  TABLE  .   157 


PRIMARY   METHODS. 


CHAPTER    I. 

THOUGHTS   BEFORE   WORDS   IN   EXPRESSION. 

tHE  life  of  man,  like  all  individual  life, 
consists  of  a  series  of  actions  and  reac- 
tions which  constitute  the  experience  of  the 
man.  They  leave  a  residue  in  his  conscious- 
ness and  in  his  manner  of  "being1.  The  former 
is  the  furniture  of  his  insight ;  the  latter, 
of  his  conduct.  By  the  former  the  man  is 
wise ;  "by  the  latter  he  is  virtuous.  Thus 
experience  furnishes  the  material  for  the 
wisdom  and  virtue  which  hold  all  worthy 
objects  of  education. 

The  tenets  of  Pestalozzian  education  con- 
cede this.  " Thing's  before  words ";  "things 
before  ideas  "  "  first  the  thing-,  then  its  sym- 
bol "  ;  "  the  intellect  rests  on  sense-percep- 
tions " — are  utterances  of  this  truth.  It  has 
been  applied,  however,  almost  exclusively 
to  the  in-leading  processes  in  the  growth 


2  PRIMARY    METHODS. 

of   intellect.      In    the   out-leading-   processes 

»^ 

we  have  been  satisfied  -with  symbols,  with, 
•words ;  we  have  ignored  the  value  of  things. 
Although  we  had  become  aware  of  the  in- 
sufficiency of  words  in  the  formation  of 
fundamental  ideas,  yet  their  inadequacy  in 
fundamental  expression  has  been  overlooked. 
The  organs  of  speech  which  express  ideas 
in  "words,  were  to  the  school  the  only  road 
for  expression  of  thought,  worthy  of  its 
notice.  The  hand  which  expresses  ideas  in 
things  has  been  neglected. 

Similarly,  it  has  been  conceded  that  in 
the  growth  of  insight,  in  the  formation  of 
accurate  ideas,  expression  is  needed  as  much 
as  impression,  that  the  intellect  owes  much 
to  the  reflex  influence  "which  comes  from 
efforts  to  formulate  knowledge  in  words. 
But  it  has  been  overlooked  that  the  more 
or  less  plastic  expression  of  ideas  by  the 
hands,  with  the  help  of  suitable  material, 
holds  to  their  formulation  in  words  very 
much  the  same  relation  that  things  hold 
to  symbols ;  that  in  expression,  too,  it  is 
necessary  to  bring  things  before  symbols; 
things  before  "words. 

Thus,  in   studying   the    cube,  with    refer- 


THOUGHTS    BEFORE    WORDS.  3 

ence  to  its  sliape,  the  cliild  will  probably 
at  first  see  the  cube,  handle  it,  use  it  in 
his  games,  and  thus  gain  many  impressions 
concerning  its  shape.  These  may  be  ex- 
pressed in  "words  or,  plastically,  in  clay. 
Both  modes  of  expression  will  react  favor- 
ably upon  the  child's  idea  of  the  shape; 
yet  there  is  no  doubt  that  the  efforts  at 
plastic  representation  will  be  the  more  ef- 
fectual mode  to  clear  his  idea  of  inaccura- 
cies and  insufficiencies.  At  every  step  the 
child  has  opportunities  to  compare  his  rep- 
resentation of  his  idea  with  the  idea  and 
with  the  original,  to  correct  faults  and  to 
supply  omissions. 

Again,  it  may  be  possible  to  give  the 
child  a  fair  idea  of  a  square  by  showing 
him  square  pieces  of  paper,  square  figures, 
square  objects,  and  by  accompanying  this 
with  judicious  instruction  and  skillful  ques- 
tioning on  the  details  of  the  form ;  yet  all 
this  is  but  the  glare  of  gas-light  compared 
with  the  noonday  light  that  is  poured 
into  the  pupil's  mind  by  the  actual  hand- 
ling of  squares,  by  using  them  in  the  con- 
struction of  other  forms,  by  drawing  squares 
singly  or  in  symmetrical  groups,  by  cut- 


4  PBIMARY    METHODS. 

ting  such  forms  from  paper,  pasteboard,  or 
wood,  "by  fashioning  them  from  clay  or 
wax. 

It  will  "be  readily  seen  that  this  hand- 
training  has  wider  aims  than  industrial 
training  in  the  various  arts.  Industrial 
training  supplies  some  particular  or  tran- 
sient need  of  self-preservation ;  -whereas  the 
aims  of  the  hand-training  here  proposed 
lie  in  general  and  permanent  self-expansion. 
Hand-training  in  this  sense  is  as  much  a 
need  of  the  professional  and  literary  man, 
of  the  merchant  and  clerk,  of  the  capitalist 
and  land-owner,  as  it  is  of  the  artist  and 
artisan,  of  the  laborer  and  farmer ;  as  much 
a  need  of  woman  as  it  is  of  man ;  its  need 
rests  on  the  immanent  being  of  man,  not 
on  transient  industrial  circumstances. 

Industrial  work  selects  its  material  pri- 
marily in  accordance  with  the  use  to  -which 
its  products  are  to  be  put,  "whereas  the 
hand-training  here  proposed  looks  prima- 
rily, in  the  selection  of  materials,  to  the 
capacities  and  needs  of  the  little  workers. 
Here  it  is  of  the  first  importance  that  the 
material  should  yield  readily  to  the  work- 
er's limited  skill.  It  should  be  of  such  a 


THOUGHTS    BEFORE     WORDS.  S 

shape  and  character  that  it  -will  adapt  itself 
without  worry  to  the  worker's  aim,  so  that 
he  may  reach  automatism  in  manual  ex- 
pression as  readily  as  he  does  in  speech ;  it 
should,  therefore,  he  so  prepared  that  the 
arranging-  and  transforming  activities  of 
the  hand  may  receive  ready  answers,  as  is 
done  to  a  large  extent  in  the  materials 
suggested  by  Froebel. 

The  business  of  life  is  adaptation  to  sur- 
roundings, to  nature,  to  the  universe.  This 
implies  knowledge  and  control  of  self  and 
surroundings.  The  business  of  education  is 
to  lead  the  young  human,  being  on  the 
surest  and  shortest  road  to  this  adaptation. 
Education  should  see  to  it  that  the  income 
of  the  senses  be  properly  interpreted  and 
appreciated  by  the  mind,  and  that  the 
tongue  and  the  hands  properly  represent 
the  mind  and  execute  its  behests.  The 
mind  should  learn  to  rely  implicitly  upon 
its  powers  to  see,  say,  and  do.  In  seeing, 
saying,  and  doing,  it  should  acquire  the 
habit  of  success,  a  calm  sense  of  power,  a 
firm  conviction  of  mastership.  This  is  pos- 
sible only,  if  head  and  hand  are  trained 
simultaneously  and  in  unison  with  each 


6  PRIMARY    METHODS. 

other ;  and  for  this  purpose  the  hand- 
training1  here  proposed  is  needed  in  the 
school. 

The  advocates  of  industrial  training  are 
met  with  the  objection  that  the  school  is 
already  loaded  down  with  work,  and  that 
it  will  be  ruinous  to  the  child  to  add  fresh 
burdens.  The  hand-training1  here  proposed 
is  not  open  to  this  objection  ;  it  removes  'bur- 
dens. It  enables  the  child  to  gain  the 
knowledge  which  the  current  subjects  of 
school  instruction  represent,  in  a  manner 
more  suited  to  his  tastes  and  powers ;  in  a 
complete,  all-sided,  active,  ideal  child-life 
in  which  he  is  upheld  and  strengthened  by 
the  constant  joy  of  success,  the  steady  glow 
of  growing  power. 

The  chief  object  of  this  book  is  to  show 
how  this  may  be  accomplished,  to  lay  be- 
fore the  teachers  the  possibilities  of  avail- 
able material,  to  indicate  its  many-sided 
applicability  to  primary  school  work,  and 
to  suggest  in  a  number  of  model  lessons 
modes  of  directing  their  life-giving  sun- 
shine into  the  school-room. 


CHAPTER    II. 

THE     COURSE     OF    STUDY. 

(5^, 

tN   tlie    work   indicated    I   shall   have   be- 
fore me  a  quasi-ideal  average  Course   of 
Study,  the  essentials  of  which  appear  in  the 
following1  considerations  : 

"  In  framing  a  course  of  study  for  Pri- 
mary and  Grammar  Schools,  it  should  he 
constantly  borne  in  mind  that  the  period 
involved  corresponds  chiefly  to  the  earlier 
portion  of  the  psychological  period  of  con- 
ception. When  the  child  enters  school  he 
is  still  gathering  perceptions,  though  upon 
some  things  he  has  quite  clear  and  compre- 
hensive conceptions ;  and  when  he  leaves 
the  Grammar  School,  his  intellect  should 
have  grown  into  a  fair  supremacy,  and  the 
dawn  of  insight  into  the  deeper  relations 
of  "being  should  he  full  upon  his  mind. 
During  the  first  years  of  school  life,  the 
subjects  of  study  should  be  of  a  character 
to  facilitate  the  formation  of  perceptions 


8  PEIMARY    METHODS. 

and  their  transition  into  comprehensive 
conceptions ;  they  should  lie  on  the  side  of 
the  concrete,  the  actual,  the  outer ;  they 
should  deal  with  facts,  with  space,  with 
objects.  They  should,  then,  gradually  merge 
into  forms  that  lie  on  the  side  of  the  ab- 
stract, the  possible,  the  inner;  that  deal 
with  principles,  with  laws,  with  time, 
steadily  leading  the  child  out  of  the  com- 
plexity of  things  into  the  simplicity  of 
thought.  *  *  *  The  essentials  of  the  outer 
•world  that  interest  man  most  nearly  in  his 
efforts  to  obtain  intellectual  control  of  his 
surroundings  are  centered  in  space  "which  in 
its  limits  involves  form,  position,  size,  direction, 
and  number.  Of  these,  number  and  size  have 
a  special  interest,  inasmuch  as  they  consti- 
tute the  chief  bridges  in  the  transition  of 
the  mind  from  outer  space  to  inner  time. 
To  these  may  be  added  color  as  an  impor- 
tant element,  depending  on  certain  relations 
of  material  surfaces  to  light.  Lying  nearer 
the  emotional  side  of  sensation,  it  has  much 
power  to  arouse  interest  in  related  elements 
of  space,  hence  its  educational  value  is  very 
great.  The  school  will,  then,  find  the  first 
subjects  for  instruction  with  reference  to 


THE    COURSE    OP    STUDY.  9 

the  pupil's  individual  development,  in  the 
provinces  of  Geometry,  Drawing,  Coloring,  and 
Arithmetic. 

"  Almost  simultaneously,  however,  the 
phenomena  of  motion  and  life  to  which 
the  changes  of  position,  direction,  size,  form, 
and  number  among-  surrounding  objects  are 
referred,  and  which  intensely  affect  the 
child's  comfort  and  welfare,  point  to  studies 
connected  with  the  provinces  of  Physics, 
Chemistry,  Natural  History,  Geography,  and  Ura- 
nography. 

"Long  before  the  child's  entrance  into 
school,  too,  the  helpful  presence  of  others 
aroused  in  his  heart  feelings  of  gratitude, 
of  affection,  and  good-will.  These  may  or 
may  not  have  been  brought  more  clearly 
to  the  child's  consciousness,  and  more  fully 
within  his  control  in  the  social  games  and 
group-work  of  the  kindergarten.  Howsoever 
this  may  be,  the  school  should  afford  con- 
stant opportunity  for  social  enterprises, 
involving  common  interests,  common  pur- 
poses, and  common  effort,  leading  to  an  in- 
terest in  the  occupations  of  men,  and  in  the 
relationships  among  men.  This  leads  to 
studies  connected  with  Sociology  and  History, 


1O  PEIMARY    METHODS. 

through  which  man  connects  himself  con- 
sciously with  the  past,  and  bases  his  life 
on  the  experience  of  earlier  days. 

"  In  all  that  relates  to  motion  and  life 
and,  consequently,  to  the  social  phases  of 
being1,  sound — lying  also  nearer  the  emotional 
side  of  sensation — plays  a  part  similar  to 
that  of  color  in  the  realms  of  space.  Con- 
nected with  rhythm  in  the  harmonious 
combinations  and  melodious  successions  of 
'music, — it  has  wonderful  power  in  freeing 
the  mind  from  the  material,  and  leading  it 
to  the  spiritual,  and  is,  therefore,  of  incal- 
culable value  in  lifting  man  to  the  highest 
planes  of  mental  life. 

"  The  chief  medium  of  the  work  is  lan- 
guage. At  the  moment  when  the  child  is 
awakened  to  self-consciousness,  language 
appears  as  the  chief  outward  reaction  of 
growing  self-consciousness  in  the  inter- 
course with  others.  Language  binds  man 
to  man,  makes  the  past  an  ingredient  of 
the  present,  and  holds  this  fast  for  a  future. 
In  the  development  of  the  intellect  and  of 
reason,  it  is  the  medium  of  thought,  the 
indispensable  condition  of  their  growth. 
Hence  language,  with  all  that  pertains  to 


THE    COURSE     OF    STUDY.  11 

it,  -will  furnisli  subjects  of  instruction  dur- 
ing the  entire  school-life."* 

In  the  details  of  the  course  the  school 
should  "be  guided  largely  by  local  and 
individual  circumstances,  needs,  and  -wants. 
In  no  case,  it  is  true,  can  the  school  afford 
to  follow  the  child  through  the  maze  of 
facts  and  phenomena,  as  they  occur  in 
nature  and  in  immediate  practical  experi- 
ence. Yet,  in  all  cases,  •  it  should  create 
around  the  child  a  "world  of  objects  and 
events,  more  or  less  idealized,  and  more  or 
less  systematized,  where  the  child  may 
attain  a  fair  understanding  of  the  essentials 
of  life  with  comparatively  little  friction; 
and,  in  all  cases,  it  should  strive  to  place 
this  world  as  fully  as  possible  within  the 
child's  control. 

"While  these  remarks  apply  equally  to 
the  Primary  and  Grammar  Schools,  it  is 
evident  that  what  I  may  have  to  say  con- 
cerning the  use  of  things  in  the  school- 
room for  purposes  of  expression  will  apply 
chiefly  to  the  "work  of  the  Primary  Grades. 
Nevertheless,  even  a  superficial  survey  of 


*  Prize  Essay:    "Application  of  the    Principles    of  Psychology 
to  the  Work  of  Teaching."     By  W.  N.   Hailmann. 


12  PRIMARY    METHODS. 

the  subjects  of  instruction  'will  show  that 
so  far,  at  least,  as  Geometry,  Drawing,  Col- 
oring-,- Physics,  Chemistry,  Natural  History, 
Geography,  and  Uranography  are  concerned, 
I  might  with  profit  follow  the  pupil  through 
the  highest  grade  in  the  grammar  school, 
aiding  him  in  expressing  thought  in  things 
as  well  as  words.  However,  this  -would  ren- 
der my  task  too  cumbersome ;  and  I  shall, 
therefore,  not  go  "beyond  the  pale  of  the 
primary  school,  save  in  an.  occasional  hint 
concerning  the  extension  of  the  work  to 
higher  grades. 


CHAPTER  III. 

SYNOPTICAL  TABLE  OF  GIFTS  AND  OCCUPATIONS- 
GIFTS  AND  OCCUPATIONS  CONTRASTED. 

<2o 

tN"  order  to  enable  teachers  to  choose  in- 
telligently the  material  for  the  needs 
of  their  pupils,  I  shall  present  in  this  chap- 
ter a  survey  of  the  so-called  gifts  and  occu- 
pations selected  and  proposed  "by  Froebel  on 
the  basis  of  considerations  essentially  in  ac- 
cordance with  the  two  preceding  chapters. 
Inasmuch  as  the  play-and-work  with  these 
things  is  to  lead  the  children  to  the  study 
and  control  of  an  external  world,  their 
formal  key  lies  in  shape.  There  is  promi- 
nent in  them,  as  a  whole,  first  a  mathe- 
matical analysis  descending  from  the  "body, 
through  the  surface  and  line,  to  the  point. 
This  is  followed  among  the  gifts  by  a  syn- 
thetical gift  in  which  from  the  point  and 
line  the  child  ascends  to  less  material  rep- 
resentations of  the  surface  and  body.  In 
the  occupations,  the  synthetic  elements  are 


14  PRIMARY    METHODS. 

so  intimately  and  prominently  interwoven 
with,  their  very  e'ssence,  that  one  is  almost 
tempted  to  treat  them  as  the  specifically 
synthetic  side  of  Froebel's  scheme. 

The  following-  synoptical  presentation,  al- 
though quite  different  from  those  generally 
accepted,  is  in  strict  accordance  with  Froe- 
bel's spirit.  I  have  no  doubt  that  he  him- 
self would  have  given  us  an  arrangement 
not  unlike  this  one,  had  he  found  time  to 
look  more  calmly  upon  the  revelations  that 
came  to  us  through  him. 

I.  GIFTS. 
A.  BODIES. 

i.   Things,    objects — (color) :      Six    colored    soft    worsted 

balls.—  First  Gift. 

ii.  Shape  :  Wooden  ball,  cylinder  and  cube. — Second  Gift, 
in.  Number: 

1.  Two  (2x2x2): 

a.  Divisibility:   Eight  one-inch  cubes,  forming  to- 

gether a  two-inch  cube. — Third   Gift. 

b.  Dimensions  :    Eight  bricks  (2  x  1  X  £  in.),  form- 

ing together  a  two-inch  cube. — Fourth  Gift. 

2.  Three  (3  x  3  x  3) : 

a.  Direction  —  (Beauty)  :  Twenty-seven  one-inch 
cubes,  forming  together  a  three-inch  cube. 
Three  of  the  cubes  are  cut  diagonally  once  into 
halves ;  and  three  are  cut  diagonally  twice  into 
quarters. — Fifth  Gift. 


SYNOPTICAL    TABLE.  13 

b.  Proportionality  and  Position  (Law) :  Twenty- 
seven  bricks  (2  x  1  X  \  in.),  forming  together  a 
three-inch  cube.  Three  of  the  bricks  are  cut 
lengthwise  once  into  square  prisms  (2  x  \  X  \ 
in.),  and  six  bricks  are  cut  crosswise  once  into 
flat  square  prisms  (1  x  1  X  \  in.). — Sixth  Gift. 
B.  SURFACES. 

i.  Squares  derived  from  third  gift,  cut  from  veneer  or 
card-board. 

1.  Entire  squares  (one  square  inch). — Seventh  Gift  A. 

2.  Half   squares,    right   isosceles   triangles. — Seventh 

Gift  B. 
n.  Equilateral  Triangles. 

1.  Entire  triangle,  each  side  one  inch  long. — Seventh 

Gift  C. 

2.  Half    triangles,   right   scalene   triangles. — Seventh 

Gift  D. 

[These  were  formerly  derived,  less  logically, 
from  a  double  square  or  oblong  rectangle, 
cut  diagonally.] 

3.  Thirds  of   triangles,  obtuse  isosceles  triangles. — 

Seventh  Gift  E. 

in.  Circles.  [The  scheme  calls  for  these,  but  as  yet  manu- 
facturers do  not  furnish  them,  nor  do  manuals  give 
directions  concerning  their  use.  With  a  one-inch 
gun-wad  cutter,  which  may  be  obtained  of  any  gun- 
smith, they  may  be  cut  cheaply  from  stiff  paper  or 
card-board.] 
C  LINES. 

i.  Straight  Line:  Sticks  or  splints  of  various  lengths. — 

Eighth  Gift  A. 

n.    Curved  Line:  Rings  and  half-rings  of  various  sizes. — 
Eighth  Gift  B. 


16  PRIMARY    METHODS. 

D.  POINTS. 

Lentil-seeds,  pebbles,  beans,  etc. — Ninth  Gift. 

E.  RECONSTRUCTION.     (Synthesis.) 

Softened  peas  and  sticks  or  straws. — Tenth  Gift. 

II.  OCCUPATIONS. 

A.  BODIES. 

1.  Plastic  clay  (or  substitutes,  such  as  wax,  putty,  etc.). 

2.  Card-board. 

3.  Sand. 

B.  SURFACES. 

1.  Folding  sheets.     (To  the  square  and  oblong  sheets,  sug- 

gested by  Froebel,  I  have  added  the  circle  and  equi- 
lateral triangle.) 

2.  Cutting  and  Pasting.     (Paper,  card-board,  wood.) 

3.  Painting.     (With  brush  or  crayon,  or  with  the  lead  or 

slate  pencil  in  "  shading.") 

C.  LINES. 

1.  Interlacing  slats. 

2.  Jointed  slats. 

3.  Intertwining  strips. 

4.  Weaving  mats. 

5.  Thread-games. 

6.  Embroidery. 

7.  Drawing. 

D.  POINTS. 

1.  Stringing  beads.     (Mrs.  Hailmann's  Second-Gift  beads.) 

2.  Mrs.  Hailmann's  lentils  or  dots. 

3.  Buttons,  papers,  and  straws,  etc. 

4.  Perforating. 

I  am  aware  that  tlie  distinction  "between 
gifts  and  occupations  is  post-Fro~belian ;  "but 


GIFTS     AND    OCCUPATIONS.  17 

it  is  not  on  that  account  less  real.  The 
gifts  are  intended  to  give  the  child  from 
time  to  tim'e  new  universal  aspects  of  the 
external  world,  suited  to  the  child's  powers 
of  comprehension.  In  the  schedule  the  es- 
sential features  of  these  are  indicated  for 
the  first  six  gifts,  "by  the  italicized  words 
introducing  the  gift.  The  occupations,  on  the 
other  hand,  furnish  the  child  with  mate- 
rials on  which  to  exercise  certain  phases 
of  skill.  Any  thing  will  do  for  an  occupa- 
tion, provided  it  is  sufficiently  plastic  and 
within  the  child's  powers  of  control ;  hut 
the  gift,  in  form  and  material,  is  largely 
determined  "by  the  cosmic  phase  to  be 
brought  to  the  child's  apprehension,  and  by 
the  condition  of  the  child's  mind.  Nothing 
but  the  first  gift  can  so  effectively  arouse  in 
the  child's  mind  the  feeling  and  conscious- 
ness of  a  world  of  individual  things  and  of 
its  own  dawning  individuality ;  but  there 
are  numberless  occupations,  in  addition  to 
those  enumerated  in  the  schedule,  that  -will 
enable  the  child  to  become  skillful  in  the 
manipulation  of  surfaces. 

The  gift  gives   the    child    a   new  cosmos ; 
the  occupation  fixes   the   impressions   made 


18  PRIMARY    METHODS. 

by  the  gift.  The  gift  invites  only  arrang- 
ing activities ;  the  occupation  invites  chiefly 
controlling,  modifying,  transforming,  crea- 
ting activities.  The  gift  leans  toward  the 
in-leading  processes,  toward  instruction ; 
the  occupation  toward  out-leading  process, 
toward  expression.  The  gift  leads  to  dis- 
covery ;  the  occupation,  to  invention.  The 
gift  gives  insight;  the  occupation,  power. 


CHAPTER   IV. 

THE  WORK  SELECTED— OUTFIT  OF  SCHOOLS. 

'ROM  tlie  mass  of  material  presented  in 
the  preceding  chapter,  I  shall  select  a 
few  gifts  and  occupations,  and  show  in  a 
series  of  somewhat  detailed  directions  and 
"model"  lessons  how  they  may  be  used  in 
the  school-room  in  such  a  way  as  to  aid 
in  rendering  the  children's  growth  com- 
pact, sound,  all-sided,  and  rounded ;  and,  at 
the  same  time,  in  giving*  them  full  and 
ready  knowledge  and  mastership  in  the  di- 
rections of  ordinary  subjects  of  instruction. 

In  this,  while  I  shall  aim  to  regard  the 
types  best  suited  to  give  an  insight  into 
the  scheme  as  a  whole,  I  shall  be  guided 
largely  by  considerations  of  expediency. 
Thus  I  shall  give  preference  to  those  that 
seem  to  stand  nearest  the  school  as  it  is, 
and  that  will  prove  most  serviceable  in  the 
ordinary  school  studies.  Again,  I  shall  con- 
sider the  cost  of  the  material,  and  put 


2O  PRIMARY    METHODS. 

more  stress  upon  occupations  that  may  "be 
procured  with  comparatively  little  expense, 
so  that  teachers  may  "be  less  exposed  to  an- 
noying opposition  on  the  part  of  conserva- 
tive friends  of  education. 

Probably  each  teacher,  according1  to  the 
circumstances  in  which  she  may  he  placed, 
will  have  to  select  again  from  my  selection. 
Possibly,  too,  some  may  be  able  to  use  ma- 
terial not  treated  in  this  volume.  In  this 
case  I  hope  my  presentations  may  be  suffi- 
ciently lucid  and  comprehensive  to  enable 
her  to  make  the  new  applications  independ- 
ently. Most  of  all  should  I  rejoice,  if  -what 
I  may  say  will  enable  and  induce  teachers  to 
reach  out  in  their  surroundings  for  new  and 
simpler  material,  to  seek  simpler  "ways  of 
applying  the  principles  that  have  guided 
me,  and  to  discover  new  avenues  of  useful- 
ness for  the  materials  I  may  present. 

In  the  order  of  the  schedule  of  the  pre- 
ceding chapter  I  shall  consider :  (1)  The 
counting-blocks,  a  modification  of  the  third 
gift ;  (2)  the  square  and  half-square  tablets ; 
(3)  the  sticks  or  splints ;  (4)  the  lentil- 
seeds  ;  (5)  sticks  and  pease ;  (6)  clay ;  (7) 
card-board  work ;  (8)  folding ;  (9)  cutting 


THE     WORK     SELECTED.  21 

and  pasting;  (10)  intertwining  strips;  (11) 
Mrs.  Hailmann's  second-gift,  beads ;  (12) 
Mrs.  H.'s  dots. 

For  various  reasons,  however,  these  will 
"be  presented  in  a  different  order,  more  in 
accordance  wi;th  the  needs  of  the  school,  as 
it  is,  Thus :  (1)  Mrs.  Hailmann's  second- 
gift  heads,  "with  special  reference  to  lessons 
in  number;  (2)  the  counting-blocks,  with 
special  reference  to  number  lessons' ;  (3)  the 
folding-sheets,  with  special  reference  to 
drawing  and  geometry ;  (4)  clay,  with  spe- 
cial reference  to  drawing,  geometry,  and 
coloring ;  (5)  cutting  and  pasting  and,  sub- 
sequently, card-board  -work,  -with  special 
reference  to  arithmetic,  geometry,  and  draw- 
ing ;  (6)  intertwining  strips,  with  special 
reference  to  arithmetic  (fractions),  geometry, 
and  drawing;  (7)  the  sticks  or  splints  and, 
subsequently,  sticks  and  pease,  with  special 
reference  to  geometry,  drawing,  and  arith- 
metic; (8)  Mrs.  Hailmann's  dots  and  lentils; 
(9)  the  square  and  half-square  tablets. 

For  the  majority  of  the  exercises,  it  is 
desirable  that  the  child  should  work  upon 
a  surface  laid  off  in  square  inches,  similar 
to  the  surface  of  a  kindergarten  table.  In 


22  PRIMARY    METHODS. 

my  own  schools  I  have  found  it  quite  sat- 
isfactory to  rule  sucli  a  net-work  with,  a 
sharp  scratch-awl  on  the  ordinary  desk- 
fronts.  For  many  exercises,  particularly  in 
group-work— though  these  are  not  indispen- 
sable— it  is  desirable  to  have  small  tables, 
thirty  inches  square  and  of  suitable  height. 
The  surface  of  these,  too,  is  ruled  with  a 
net-work  of  square-inches,  and  each  table 
accommodates  four  children.  For  my  own 
schools  I  have  been  able  to  procure  such 
tables  at  a  trifling  cost  of  $1.50  a  piece, 
and  suitable  low  stools  at  $2.50  per  dozen. 
Other  matters  of  outfit  will  be  mentioned 
in  the  proper  places. 


CHAPTER   V. 

THE   SECOND-GIFT   BEADS.* 

(HE  Second-Gift  Beads  consist  of  wooden 
cubes,  cylinders,  and  balls  (the  shapes 
of  Froebel's  Second  Gift),  one  half  inch  in 
diameter,  colored  in  the  hues  of  the  rain- 
bow— red,  orange,  yellow,  green,  "blue,  violet, 
— and  perforated  for  stringing. 

For  the  school,  they  are  particularly 
useful  in  number  lessons.  The  contrasts  of 
color  and  form  afford  effective  means  for 
presenting  analyses,  aiding  the  mind  through 
the  "sub-conscious"  in  the  formation  of  clear 
notions  and  ready  mastership.  This  will 
become  evident  if  we  compare  the  follow- 
ing three  typical  ways  of  presenting  the 
number  five: 

(1)  Five  cubes  (five  cylinders,  or  five  balls) 
of  the  same  color. 

(2)  Two   pairs    of  cubes    separated   by  one 
ball,  all  of  the  same  color. 

*  Mrs.  Hailmann's  Second-Gift  Beads   are   manufactured  by  the 
Milton  Bradley  Company,  of  Sprinarfleld,  Mass. 


24  PRIMARY    METHODS. 

(3)  Two  pairs  of  red  "balls  separated  by  a 
green  ball. 

In  the  first  mode  (1)  it  will  be  found 
that  the  little  child  can  not  arrive  at  the 
unit :  five  balls  (or  beads),  without  laboriously 
counting :  one,  two,  three,  four,  five.  This 
process  constantly  tempts  him  to  look  upon 
these  counting  numbers  as  names,  and  to  call 
the  first  ball  one;  the  second,  two;  the  third, 
three,  etc.  Thus  the  very  unity  in  the  outer 
fact  hinders  the  growth  of  the  desired 
corresponding  mind  unit.  In  the  second 
mode  (2)  the  contrast  in  form  breaks  up  the 
number  five  into  the  familiar  constituents, 
2  +  1  +  2  ;  and  these  are  readily  united  by 
the  common  color  into  five  BEADS.  Similarly, 
in  the  third  mode  (3),  the  separation  into 
2  +  1  +  2  is  made  by  color,  and  the  common 
form  unites  the  beads  into  five  BALLS. 

Another  important  feature  of  the  work 
lies  in  the  possibility  of  arranging1  the  beads 
in  rhythmic  waves  of  form,  color,  and  num- 
ber. This  is  illustrated  in  the  following 
lesson  of  threes,  in  "which  the  square  ([  [) 
stands  for  cube ;  the  circle  (O)>  ^or  "ball  '•>  the 
semicircle  (Q),  for  cylinder;  and  the  let- 
ters for  the  colors  (r  for  red,  o  for  orange, 


THE     SECOND-GIFT     BEADS.  25 

y  for  yellow,  g  for  green,  6  for   blue,  and  v 
for  violet) : 


In  tnis  exercise  two  waves  are  repre- 
sented, separated  from  eacli  other  "by  a 
green  bead  at  the  point  S.  The  color  wave 
on  each  side  of  this  bead  is  as  follows : 
(r-o-y)  (g-b-b)  (v-v-v)  (b-b-g)  (y-o-r).  The  cor- 
responding form  Avave  will  be  easily  read 
from  the  diagram.  The  number  wave  reads, 
(1  +  1  +  1)  (1  +  2)  (3)  (2  +  1)  (1  +  1  +  1).  It  will 
be  seen  that  the  second  half  of  the  wave 
is  in  arrangement  the  reverse  of  the  first 
half,  descending  where  the  latter  ascends. 

The  outfit  for  the  class  is  simple.  Each 
child  is  furnished  with  a  box  of  50-100  as- 
sorted beads,  and  a  shoe-string,  two  or  three 
feet  long.  This  outfit  is  ample  for  all  ex- 
ercises within  the  limits  of  1  and  10,  and 
admits  of  many  exercises  beyond  these 
limits.  For  a  class  of  twenty  children  the 
cost  will  not  exceed  $2.00.  One  end  of  the 
shoe-string  is  tied  to  some  convenient  part 


26 


PRIMARY    METHODS. 


of  the  desk  or  table,  and  the  other   end    is 
used  for  stringing  the  beads. 

The  beads  may  be  used  for  all  funda- 
mental operations  within  the  limits  of  one 
and  ten,  and  one  and  twenty.  In  proof  of 
this  I  suggest  below  several  series  of  exer- 
cises in 

(1)  Counting  by  ones,  twos,  threes,  fours, 
and  fives. 

(2)  Analyses  and   syntheses    of  the   num- 
bers two  to  ten. 

(3)  The  making  of  addition   and  subtrac- 
tion tables. 

(4)  The  making  of  multiplication  and  di- 
vision tables. 

In  the  exercises  the  arrangement  of  the 
beads  will  be  indicated  with  the  help  of 
the  symbols  already  mentioned,  and  the 
respective  number  lesson,  indicated  in  fig- 
ures, will  accompany  each  exercise. 

I.   COUNTING  EXERCISES. 
l.\g[r}g[r]glr]g  (r^HYr}&c^ 

d, 


THE    SECOND-GIFT    BEADS. 


27 


(1,  2)  (1,  2)  (1:  2)  &c. 


6. (y\r ]v    r    2/Yrly    r    j/Yr    &c. 


^(1,2,3) 
,2,3) 


10. 


(1,  2,  3,  4)  (1,  2,  3,  4)  (1,  2,  3,  4)  &c. 


^)Q0gX^  &c. 

(2, 4)  (2, 4, 6)  (2, 4, 6, 8)  &c. 


28 


PRIMARY    METHODS. 


(4,8,13 4,8,12) 


(5,10,15)&c. 


^  (1,2, 3,4, 5— 
5,4,3,2,1) 


In  the  first  three  exercises,  the  members 
of  each  pair  of  heads  differ  both  in  color 
and  shape,  and  the  child  recognizes  them 
merely  as  "two  ones,  or  (1,  1).  It  will  prob- 
ably count,  e.  g.,  in  Exercise  1  :  "  one  green 
cube,  one  red  ball ;  one  green  cube,  one  red 
ball,"  etc. 

In  the  Exercises  4,  5,  and  6,  on  the  other 
hand,  the  members  of  each  pair,  though 
separated  by  color  into  two  ones  —2(1)—, 
are  united  by  shape  into  one  two  - 1(2). 
Reading  the  fourth  exercise  by  color,  the 
child  would  say:  "One  red  cube,  one  blue 
cube;  one  red  ball,  one  blue  ball,"  etc.;  or 
simply:  "One  red,  one  blue,"  etc.  Reading 
the  same  exercise  by  shape,  it  would  say: 
"  Two  cubes,  two  balls,"  etc. 


THE    SECOND-GIFT    BEADS.  29 

Similarly,  in  Exercises  7  and  8,  the  mem- 
bers of  each  set  of  three  differ  both  in  color 
and  shape.  The  child  "would  count,  while 
stringing1  (in  Exercise  7) :  "  One  blue  cube, 
one  red  cylinder,  one  yellow  ball,"  etc.  On 
the  other  hand,  in  Exercises  9  and  10,  the 
shape  gathers  the  beads  into  distinct  sets 
of  threes.  The  child  would  read  while 
stringing-  (Exercise  9) :  "  One  red  cube,  one 
orange  cube,  one  yellow  cube"  etc. ;  or  by 
shape  alone :  "  One  cube,  two  cubes,  three 
cubes,"  etc.  When  the  string  is  finished,  it 
will  read  from  its  work,  by  shape :  "  Three 
cubes,  three  cylinders,  three  balls,"  etc. 

Similar  remarks  apply  to  Exercises  11, 
12,  13,  and  14.  In  Ex.  13,  the  reader  will 
observe  color  waves,  the  color  ascending  in 
each  group  of  five  from  red  to  yellow,  and 
descending  on  the  opposite  side  from  yellow 
to  red.  In  Ex.  14,  the  color  waves  of  each 
group  of  five  are  gathered  in  a  larger  form 
wave  ascending  from  the  balls  to  the  cubes, 
and  descending  on  the  opposite  side  from 
the  cubes  to  the  balls.  A  second  wave  may 
be  added  to  this,  after  indicating  the  close 
of  the  first  by  means  of  a  cube,  clearly  con- 
trasting in  color  with  the  orange  balls. 


SO  PRIMARY    METHODS. 

In  Ex.  15 — counting  by  twos — the  color 
separates  the  "beads  into  sets  of  twos ;  and 
the  shape  teaches  the  child  to  read  suc- 
cessively, as  it  strings  the  beads  or  surveys 
its  work :  "Two,  four  (cubes)";  "two,  four, 
six  (balls) ;  two,  four,  six,  eight  (cylinders)." 
Here  the  child  may  insert  an  orange  ball, 
in  order  to  mark  the  highest  point  of  the 
number  wave,  and  then,  reversing  the  or- 
der of  colors  and  shapes,  count :  "  two,  four, 
six,  eight  (cylinders)  *  two,  four,  six  (balls) ; 
two,  four  (cubes),"  etc. 

Ex.  16  and  17  suggest  the  counting  by 
threes.  In  Ex.  16,  the  child  counts:  "three, 
six,  nine  (balls) ;  three,  six,  nine  (cubes) " ; 
and  repeats  this  counting  at  pleasure.  Here 
shape  unites  the  threes,  and  color  keeps 
them  distinct.  In  Ex.  17,  the  reverse  is 
the  case ;  color  unites  the  threes,  and  shape 
keeps  them  distinct.  Here  the  child  counts : 
"  three,  six,  nine  (blue  beads) ;  three,  six, 
nine  (yellow  beads) ;  three,  six,  nine  (red 
beads)," — and  repeats  the  exercise  at  pleasure. 

In  Ex.  18,  shape  unites  the  fours.  The 
exercise  presents  coinciding  shape  and  color 
waves,  the  highest  point  being  marked  by 
&  green  cube.  The  child  counts  :  four,  eight, 


THE    SECOND-GIFT    BEADS.  31 

twelve  (cylinders) ;  four,  eight,  twelve  (cyl- 
inders). It  goes  without  saying  that  the 
green  cube,  marking  the  highest  point  of 
the  wave,  is  not  counted ;  also,  that  "before 
the  exercise  is  repeated,  an  orange  hall 
must  "be  strung  to  separate  the  last  "blue 
cylinder  of  the  first  exercise  from  the  first 
blue  ball  of  the  repetition. 

In  Ex.  19,  color  unites  the  fives.  The 
highest  point  of  the  shape  wave  is  indi- 

• 

cated  by  a  yellow  cube.  The  child  counts : 
five,  ten,  fifteen  (red  beads) ;  then — omitting 
to  count  the  yellow  cube — five,  ten,  fifteen 
(red  beads).  The  repetition  of  the  exercise 
would  call  for  a  green  ball  to  separate  the 
two  exercises. 

Exercise  20  is  an  excellent  counting  ex- 
ercise. It  reads— both  in  color  and  shape : 
"  One  (orange  ball),  two  (yellow  cylinders), 
three  (green  cubes),  four  (blue  cylinders),  five 
(violet  balls) "  ;  and  from  the  red  cube  down- 
ward: "Five  (violet  balls),  four  (blue  cylinders), 
three  (green  cubes),  two  (yellow  cylinders),  one 
(orange  ball)." 

I  trust  that  these  suggestions  and  expla- 
nations will  make  it  easy  for  the  teacher 
to  devise  additional  exercises,  as  they  may 


32  PRIMARY     METHODS. 

be  needed.  Tlie  exercises  may  "be  dictated 
orally  to  the  children ;  or  they  may  "be  in- 
dicated on  the  "blackboard  with  the  help 
of  the  symbols  used  in  this  book ;  or  the 
children  may  be  left  to  invent  form  and 
color  combinations  for  given  number  for- 
mulas. The  last,  however,  should  not  be 
indulged  too  soon  nor  too  frequently. 


CHAPTER    VI. 

SECOND-GIFT     BEADS.     (Conclusion.) 

'ROM  the  very  nature  of  tlie  opposite 
processes,  analysis  and  synthesis,  it 
follows  that  the  same  exercises  will  answer 
the  purposes  of  "both.  The  inspection  of 
the  following-  typical  exercise  with  the 
number  three  will  show  this : 


(14-1-1-1)  (1+2)  (2+1)  (3)  (1+2)  (2+1)  (1  +  1+1) 

This  may  be  read  from  left  to  right  syn- 
thetically :  1  +  1  +  1  =  3,  1  +  2  =  3,  2  +  1  =  3, 
3  =  3,  1  +  2  =  3,  2  +  1  =  3,  1  +  1  +  1  =  3.  Or, 
it  may  be  read,  in  the  same  direction  ana- 
lytically :  3  =  1  +  1  +  ],  3  =  1  +  2,  3  =  2  +  1, 
3  =  3,  3  =  1  +  2,  3  =  2  +  1  =  3  =  1  +  1  +  1. 

Inasmuch  as  the  stringing  of  the  beads 
is  a  synthetic  process,  it  will  be  necessary 
to  begin  -with  the  synthetic  reading.  As 
the  child  proceeds  with  the  work  of  string- 


34  PRIMARY    METHODS. 

ing-  the  beads,  it  says  in  accordance  with 
the  teacher's  dictation  or  with  the  number 
formula  indicated  on  the  blackboard :  "  One 
orange  (ball),  one  green  (ball),  one  violet 
(ball) — three  balls ;  one  red  (cyl.),  two  green 
(cyl.) — three  cylinders ;  two  blue  (cubes),  one 
yellow  (cube)  —  three  cubes;  three  violet 
balls,"  etc. 

When  the  work  is  clone,  it  surveys  the 
string  of  beads,  and  is  helped  to  read  ana- 
lytically, from  left  to  right  or  vice  versa : 
"  Three  balls — one  orange,  one  green,  one 
violet ;  three  cylinders— one  red,  two  green ; 
three  cubes — two  blue,  one  yellow ;  three 
violet  balls,"  etc. 

Similar  remarks  apply  to  the  "  tables " 
for  addition  and  subtraction,  as  well  as  to 
those  for  multiplication  and  division.  The 
bead  exercise  that  answers  for  addition  is 
equally  serviceable  for  subtraction ;  and  the 
exercise  that  teaches  multiplication  is 
equally  useful  for  division,  as  will  appear 
directly. 

II.   SYNTHESIS  AND  ANALYSIS  OF  2  TO  10. 


SECOND-GIFT    BEADS. 


3. 


«"|  y  I  v  I  y  P)  1  (i+i+i)  (1+2)  (2+i) 

I      (3) -(3)  (1+2)  or  3 

^YoYwYffYbYi^      I    Jstifi'  &c.1  + 

.    .A.     yV    ^  I  '  ' 


(2+2)  (4) 
(  2  +  3  ) 
&c.;— or, 


I       4  =  4(1),  4  =  1+3,  4  =  2(2),  4  =  1(4),  &c. 


5. 


(1+2+1)  (1+3)  (2+2)  (3+1)  (4)  &c. 


ol   &c.  5  (1)  (1+2. 


+2)  (1+3+1)  (1+4)  (2+3)  (5)  (3+2)  (4+1)  &C; 


FW^^^ 


V    o     r  I  ,     6  (1),  3  (2),  2  (3),  (6),  2  (3),  3  (2),  6  (1) 


9. 


(vXty^^^ 


•     (H-5)  (3+4)  (3+3)  (6)  (3+3)  (4+2)  (5+1) 


36 


PRIMARY    METHODS. 


10. 


y  \y 


y  \V 


.      (3+4)  (2+5)  (1+6)  (7)  (6+1)  (5+2)  (4+3) 


11: 


(33510^^  (44-4),  (3+5) 


13. 


0    Z>    b    v  171 


14. 


o 

o 

0 

'J 

<J 

g 

V 

V 

v 

0 

0 

0 

0 

0 

0 

o 

0 

0 

oj^rj   &c.  2  (4),  4  (2),  8  (1),  8,  8  (1)  Sec. 

3©@^ 
&c.  3  (3),  9  (1),  9,  &c. 


15. 


y    r    y    r\    &c.  a  (5),  5  (2),10  (1),10,10(1)  &c. 


All  tliese  exercises  may  "be  read  analytic- 
ally   as   well    as    synthetically.      Thus    Exer- 


SECOND-GIFT    BEADS.  37 

else  10  may  be  read,  3  +  4  =  7,  2  +  5  =  7, 
1+6  =  7,  7  =  7,  6  +  1  =  7,  5  +  2  =  7,4  +  3  =  7; 
or,  analytically,  7  =  3  +  4,  7  =  2  +  5,7=1  +  6, 
7  =  7,  7  =  6  +  1,  7  =  5  +  2,  7  =  4  +  3.  This  is 
indicated  above  in  Ex.  2,  3,  and  4. 

After  what  has  been  said  011  the  subject 
in  Chapter  V.,  the  teacher  will  find  it  easy 
to  discover  the  suggestions,  indicated  in  the 
diagrams,  concerning  waves  of  color  and 
form,  as  well  as  the  devices  for  marking 
the  highest  points  of  the  waves  and  for 
separating  one  wave  from  another.  Thus, 
Ex.  1  indicates  two  waves  separated  by  a 
purple  cylinder ;  and  in  Ex.  3  the  highest- 
point  of  the  wave  is  marked  by  a  red  ball. 
In  most  cases  only  one  wave  is  indicated, 
as  in  Ex.  2,  3,  4,  and  5.  In  some  cases, 
only  a  part  of  the  wave  is  shown ;  the 
teacher  will  find  it  easy  to  supply  the 
missing  "  descending "  portion,  e.  g.  in  Ex. 
6,  7,  and  others.  In  all  cases,  pupils  may 
string  as  many  "waves  as  time  and  beads 
permit. 

It  will  be  noticed  that,  in  exercises  with 
numbers  above  5,  the  number  itself  "which 
marks  the  highest  point  of  the  "wave  in 
beads  of  the  same  color  is  broken  up  into  a 


38 


PRIMARY    METHODS. 


shadowy  form  wave.  This  is  done  in  order 
to  enable  the  child  to  recognize  the  num- 
ber more  readily  and  without  counting  ~by  ones. 
Thus,  in  Ex.  8,  the  six  purple  beads  in  the 
middle  are  two  cylinders  with  two  cubes  on 
each  side.  These  "  three  twos "  indicated 
by  the  differences  of  form,  facilitate  the 
reading  of  the  "six  purple  beads."  This 
device  should  be  dropped  very  cautiously, 
inasmuch  as  children  find  it  quite  difficult 
to  grasp  at  sight  numbers  higher  than  five. 

III.  ADDITION  AND  SUBTRACTION  TABLES. 


r    o 


&c. 

"'1(2-1)  (3-1)  (4-1)  (5-1)  (6-1)  &c. 


(2+2)  (3+2)  (4+2)  &c.— (3-2)  (4-2)  (5-2)  (6-2)  &c. 


(6-3)  (7-3)  &c. 


&c-   (1+3)  (2+3)  (3+3)  &c.-(4-3)  (5-3) 


&c.   (1+2)  (3+2) 


(5+2)  &c.— (3-2)  (5-2)  (7-2). 


r   r   wi»lwrrTrTrTTT«T«Y0TrirTr.TrYrirY»it»ic 


&c.  (2+3)  (4+3)  (6+3)  &c.— (5-3)  (7-3)  (9-3)  &c. 


SECOND-GIFT    BEADS.  39 


ft  I  b  I  g  |  g  |  g"|TybY^Y^Y^l  &c.(2+i) 


(2+2)  (2+3)  (2+4)  &c.-(6-2)  (5-2)  (4-2)  (3-2). 

V\V\  &c.(3+l) 


oYoYoYVToYoro  TVTVIV1O  o 


(3+3)  (3+5)  &c.-(8-3)  (6-3)  (1-3). 


For  the  addition  and  subtraction  exer- 
cises, it  is  not  desirable  to  reverse  the  order 
of  tne  exercises,  or  to  string  tne  "beads  in 
•waves  of  color  and  form.  Each,  repetition 
of  an  exercise  should  be  in  the  same  order 
with  the  first,  ascending  or  descending ; 
only  in  the  colors  of  the  beads  a  change 
should  be  made.  Thus,  in  a  repetition  of 
Ex.  1,  the  beads  would  follow  each  other 
in  the  same  order  and  arrangement  [(1  +  1) 
(2  +  1)  (3  +  1),  etc.] ;  but  for  red  and  orange 
two  other  adjacent  colors,  e.  g.,  blue  and 
violet,  would  be  used.  Then,  for  a  third 
series,  yellow  and  green  may  be  chosen. 

It  will  be  noticed  that  in  all  exercises 
sharp  color  contrasts  bet-ween  the  terms  of 
the  same  sum  or  series  of  sums  (or  differ- 
ences) are  avoided.  This  facilitates,  on  the 
one  hand,  the  formation  of  mental  sum 
images,  and  minuend  images.  For  similar 
reasons,  the  same  color  contrasts  are  re- 


4O 


PRIMARY    METHODS. 


tained  for  a  given  series  of  sums  or  differ- 
ences. 

It  'will  l)e  easy  for  the  teacher  to  dis- 
cover the  principles  that  underlie  the  con- 
struction of  Ex.  1,  2,  and  3 ;  4  and  5,  and  6 
and  7,  respectively ;  and  to  construct  what- 
ever additional  similar  exercises  she  may 
desire  for  the  same  or  other  numbers.  Still 
other  tables  in  which  the  sum  (respectively 
the  minuend)  remains  the  same  throughout 
the  series  are  suggested  by  Ex.  9,  10,  and 
12,  on  pp.  35  and  36. 

IV.   MULTIPLICATION  AND  DIVISION  TABLES. 


a. 


&c.  2(l),2(2),.2(3),.2(4)&c.~ 


2.     v 


3  (2),  3  (3),  3  (4)  &c. 


r    r    r    o  \o\o\y\y    y\g    g    g  \,  &c.  4  (1),  4  (2),  4  (3)  &c. 


o    o    r 


&c.  1  (2),  2  (2),  3  (2),  4  (2)  &C. 


r    r|o|o|o|V|l/|«|g|g|g[ ,  &C.-1  (3),  3  (3),  3  (3)  &c-. 


SECOND-_GIFT    BEADS.  41 

»E0®S)®(^^ 


In  Ex.  1,  2,  and  3  the  multiplier  is  con- 
stant ;  in  Ex.  4  and  5  the  multiplicand  is 
constant ;  in  Ex.  6  the  product  is  constant. 
Additional  suggestions  for  the  last  case  may 
"be  found  in  Ex.  13,  14,  and  15,  on  page  36. 

The  exercises  may  be  dictated  or  indi- 
cated on  the  blackboard,  read  or  reduced 
to  slate-work  from  the  strings  for  multi- 
plication, division,  or  part-taking.  Thus, 
Ex.  1  may  be  dictated  or  indicated  on  the 
blackboard. 

(a)  for  multiplication.  (b)  for  division.  (c)  for  part-taking. 

2  (1)                              2-1-1  *  1  (2)    or    1  (2) 

2  (2)                               4-5-2  I  (4)  i  (4) 

2  (3)                               6-f-3  |  (6)  1  (6) 

2  (4)                               8-1-4  |  (8)  i  (8) 

etc.                           etc.  etc.  etc. 

The  child  may  read  the  answers  from  the 
string,  for  multiplication :  Two  ones  are 
two,  two  twos  are  four,  etc. ;  for  divi- 
sion :  There  are  two  ones  in  two,  there  are 
two  twos  in  four,  etc. ;  for  part-taking :  Two 

*  This   is   read   by  the    pupil    from   right  to  left :    ' '  How  many 
ones  in  two?   how  many  twos  in  four,"  etc. 


42  PRIMAEY    METHODS. 

halves  of  two  are  two  ones,  two  halves  of 
four  are  two  twos;  or  one  half  of  two  is 
one,  one  half  of  four  is  two,  etc.  —  It  may 
reduce  the  results  of  its  stringing  to  slate- 
work  as  follows  : 

(a)  for  multiplication  ;  (b)  for  division  ;  (c)  for  part-taking. 


(4)=2 
(6)=3 
(8)=4 
(10)=5 
etc. 


The    following    additional  dictations    are 

suggested  for  the  benefit  of  the    less    expe- 
rienced teachers  : 

(a)  for  multiplication  ;        (b)  for  division  ;  (c)  for  part-taking. 


2  (1)=   2 

2-1=2  (1) 

1    (2)=2  (1) 

2  (2)=  4 

4-2=2  (2) 

1    (4)=  2  (2) 

2  (3)=   6 

6-3=2  (3) 

1     (6)=2  (3) 

2  (4)=  8 

8-4=2  (4) 

1     (8)=2  (4) 

2  (5)=10 

10-5  =  2  (5) 

|  (10)=2  (5) 

etc. 

etc. 

etc. 

1)  3  (1) 

2)  4  (1) 

1)  3-1 

2)  4-1 

1)  1  (3) 

2)  |  (4) 

3  (2) 

4  (2) 

6-2 

4-2 

1(6) 

1(8) 

3(3) 

4  (3) 

9-3 

4-3 

1(9) 

i  (12) 

3  (4) 

12-4 

4-4 

1(12) 

3)  1  (2) 

4)  1  (3) 

3)  2-2 

4)  3-3 

3)  f  (4) 

4)  I  (6) 

2  (2) 

2  (3) 

4-2 

6-3 

1(6) 

1(9) 

3  (2) 

3  (3) 

6-2 

9-3 

1(8) 

1(12) 

4  (2) 

3  (4) 

8-2 

12-3 

5  (2) 

10-2 

5)  1  (4) 

6)  1  (5) 

5)  4-4 

6)  5-5 

5)  f  (8) 

6)  |  (6) 

2  (4) 

2  (5) 

8-4 

10-5 

1(8) 

1(6) 

3(4) 

3(5) 

12-4 

15-5-5 

1(8) 

1  (6) 

SECOND-GIFT    BEADS. 


43 


The  child  would  read  the  answers  from 
the  string,  as  indicated  on  page  41.  In 
slate-work,  the  answers  would  make  neat 
tables,  as  follows : 


(a)  for  multiplication  ; 

(b)  for  division  ; 

1)  3  (1)=   3 

2)  4  (1)=  4 

1)  3-5-1  =  3  (1) 

2)  4-5-1=4  (4) 

3  (2)=   6 

4  (2)=   8 

6-*-2=3  (2) 

4-f-2=2  (2) 

3  (3)=   9 

4  (3)=12 

9-5-3  =  3  (3) 

4-^-3  =  1  (3)  +  l 

3  (4)=  12 

12-5-4=3  (4) 

4-5-4=1  (4) 

3)  1  (2)=   2 

4)  1  (3)=   3 

3)  2-*-2  =  l  (2) 

4)  3n-3  =  l  (3) 

2  (2)=   4 

2  (3)=   6 

4n-2=2  (2) 

6-5-3  =  2  (3) 

3  (2)=   6 

3  (3)=   9 

6-i-2  =  3  (2) 

9-5-3  =  3  (3) 

4  (2)=   8 

3  (4)=  12 

8-5-2=4  (2) 

12n-3=4  (3) 

5  (2)=10 

10n-2=5  (2) 

5)  1  (4)=   4 

6)  1  (5)=   5 

5)  4-^4=1  (4) 

6)  5-5-5=1  (5) 

2  (4)=   8 

2  (5)=10 

8-5-4=2  (4) 

10-5-5=2  (5) 

3  (4)=12 

3  (5)=15 

12-5-4=3  (4) 

15-*-5=3  (5) 

(c)  for  part-taking. 

1)  |    (3)=3  (1)  2)  |    (4)=4  (1) 

|     (6)=3  (2)  £     (8)=4  (2) 


3) 


5) 


f     (9)=3  (9) 
i  (12)=3  (4) 

|  (12)=4  (3) 

1     (4)=2  (2) 
i     (6)=3  (2) 
1    (8)=4  (2) 

4)  |  (6)=2  (3) 
1  (9)=3  (3) 
f  (12)=4  (3) 

1    (8)=2  (4) 
1    (8)=4  (2) 
t    (8)=8  (1) 

6)  |  (6)=2  (3) 
1  (6)=3  (2) 
t  (6)=6  (1) 

44  PRIMARY    METHODS. 

It  will  rarely  be  found .  advisable  to  go 
beyond  ten  in  these  exercises.  Even  the 
twelves  and  the  fifteens  in  the  above  sug- 
gestions are  of  doubtful  propriety. 

Work  of  this  character  may  be  done  with 
great  profit  during  the  first  (average)  school- 
year,  and  need  not  be  wholly  abandoned 
during  the  second  school-year. 


CHAPTER    VII. 

A  NUMERAL   FRAME   FOR   EACH   PUPIL. 

G±t 

tN  a  measure,  tlie  exercises  suggested  in 
the  last  two  chapters  satisfy  this  de- 
mand of  "a  numeral  frame  for  each  pupil." 
Yet,  while  they  are  unsurpassable  for  the 
formation  of  number  perceptions,  more  flexi- 
ble material  is  needed  for  calling  up  more 
promptly  and  in  quicker  succession  images 
of  these  perceptions  in  the  mind,  thus  aid- 
ing in  the  formation  of  mobile  number  con- 
ceptions, and  leading  the  pupil  from  the 
mere  desire  for  playing  with  numbers  of 
pretty  things  to  a  real  interest  in  number 
as  such. 

For  this  purpose  I  have  chosen  the  balls. 
They  represent  the  most  mobile  of  the 
three  bead  forms  and  are  least  weighted 
•with  form  features..  These  again  are  grad- 
ually freed  from  disturbing  color  contrasts 
by  giving  the  pupil  only  two  colors  to 
.work  with,  separating  the  ten  beads  of  the 


46  PRIMARY    METHODS. 

first  series  of  exercises  into  two  fives,  and 
the  twenty  beads  of  the  second  series  into 
two  tens.  These  beads  are  fixed  on  the 
child's  desk  in  a  mobile  arrangement,  con- 
stantly ready  for  immediate  use  (Fig.  1). 
Near  the  back  of  the  desk  two  eyelet  screws 


are  screwed  into  the  desk.  To  one  of  these 
a  shoe-string  is  tied.  The  beads  are  then 
strung  by  the  pupil,  and  the  free  end  of  the 
string  tied  with  a  bow-knot  to  the  second 
screw.  The  entire  outfit  costs  five  cents. 

In  all  arithmetical  exercises,  this  contriv- 
ance is  at  hand  to  furnish  the  child  "with 
the  sure  foundation  of  actual  number  per- 
ceptions, to  give  him  opportunities  for  trans- 
lating his  number-thoughts  into  things,  and 
to  shield  him  against  the  dangers  of  mere 
verbalism.  With  its  help  the  pupil  follows 
dictations,  solves  problems  indicated  on  the 
board  or  in  the  book,  studies  the  relation- 
ships of  given  numbers,  prepares  arithmet- 


A  NUMERAL  FRAME  FOR  EACH  PUPIL.   47 

ical  tables,  etc.  A  few  typical  exercises  will 
illustrate  my  meaning-.  The  exercises  are 
selected  from  the  first  series  for  ten  "beads 
or  two  fives. 

(1)  The  teacher  is   ready   to    dictate  this 
exercise  :    2  +  3  —  4  +  3' +  2  —  1  +  3  +  2.     The 
children  sit  ready  to  give  the  answers,  first 
on    the    strings   of  "beads,    and   then   orally, 
as  follows  (the  teacher's  words  are  quoted) : 
"  Place    all    "beads    on    the    left.      With   the 
right  hand  move  to  the  right :  Two  "beads." 
—Two    "beads.— "Add   three."— Five    (beads).— 
"Subtract  four."— One  (bead).— "Acid  three." 
—Four    (beads).— "  Add    two."— Six    (beads).— 
"Subtract  one."— Five  (beads).— "  Add  three." 
—Eight  (beads).— "  Add  two."— Ten    (beads).— 
The    same    exercise    may   then    be    repeated 
with    the   left   hand,   moving   the   beads   to 
the  left.     Indeed,  in  the  light   of  the   ben- 
eficial influence  of  ambidextrous  work  upon 
mental   growth,    I   am   tempted   to    say  the 
exercise  should  be  so  repeated. 

(2)  The    teacher    has    decided    upon    this 
dictation :     1  +  3,    2  +  2,     1  +  4,     2  +  3,     4  —  3, 
5-3,.    3  +  1,    4  +  1,    5-1,    4-2,    3  +  2,    5-2. 
The  children  sit  ready  as  above.    The  teacher 
begins :    "  With  the  left   hand,  all   beads   to 


48 


PRIMARY    METHODS. 


the  left. — With  the  right  hand  one  bead, 
with  the  left  hand  three  "beads;  move  all 
to  the  right." — Children,  as  they  move  the 
"beads :  One  ("bead)  and  three  (beads)  are  four 
(beads).— "  All  beads  to  the  left."— (It  should 
be  understood  that  this  is  carried  out  "with 
the  left  hand).—"  (With  the  right  hand)  two 
beads,  (with  the  left  hand)  two  beads ;  (all 
to  the  right)." — Two  (beads)  and  two  (beads) 
are  four  (beads). — "Beads  to  the  left."— "One 
(bead)  and  four  (beads)."— One  and  four  are 
five,  etc.  Expressions  in  parentheses  may 
be  gradually  dropped,  in  order  to  give  more 
and  more  prominence  to  the  pure  number 
forms.  The  teacher,  however,  should  fre- 
quently return  to  them. 

(3)  The  teacher  has  placed  on  the  black- 
board, for  silent  work,  one  or  more  of  the 
following  exercises : 


(1)          (2) 

(3)              (4) 

(5) 

(6) 

4 

(1) 

4 

(4) 

5  +  2  = 

4+     =6 

5 

(2) 

6 

(2) 

6-3  = 

7-     =3 

3 

(3) 

5 

(6) 

3(3)  = 

2()    =6 

6 

+  2      2 

(4) 

3 

H-2            i 

(8) 

6+2  = 

8-H4  = 

2 

(5) 

2 

(10) 

i(6)  = 

iO    =2 

7 

(3) 

8 

(6) 

|(6)  = 

5+     =8 

1 

(1) 

7 

(2) 

6-s-3  = 

6n-2  = 

8 

(4) 

9 

(4) 

5  +  4  = 

10    =4 

A  NUMERAL  FRAME  FOR  EACH  PUPIL.    49 

The  children  either  study  these  problems 
for  oral  work,  sitting  squarely  "before  the 
beads  and  working  with  both  hands  as 
occasion  may  require ;  or  they  set  down  on 
their  slates  the  problems  and  solutions, 
working  the  beads  with  the  left  hand,  and 
writing  with  the  right  hand.  Thus  : 

(1)  (2)  (3)  (4)  (5)  (6) 

4  +  2=6  2(1)=2     4-^2  =  2(2)  J(4)    =2  5  +  2  =  7       4  +  2  =  6 
4-2  =  2  2(2)=4     6-4-2  =  3(2)  1(2)    =1  6-3  =  3       7-4=3 

5  +  2  =  7  2(3)=6     5-1-2=2  (2)+ 1  t (6)    =3  3  (3)=9       2  (3)  =6 
5-2  =  3  2 (4)  =  8     3-s-2  =  l(2)  +  l  i(8)    =46-5-2  =  3(2)8-5-4=2(4) 

6  +  2  =  8  2  (5)=10  2-*-2  =  l(2)  i(10)=5  i  (6)=2       i(8)  =2 

When  the  children  have  satisfactorily 
mastered  the  first  series  of  exercises  -within 
the  limits  of  one  to  ten  or  two  fives,  they 
may  proceed  to  the  second  series,  using 
twenty  beads  or  two  tens  of  different  colors. 
These  give  very  much  greater  latitude  for 
exercises  in  multiplication,  division,  and 
part-taking. 

The  difference  in  color  in  the  two  tens 
gives  a  marked  advantage  in  the  formation 
of  clear  notions  of  numbers  between  10  and 
20.  With  red  and  green  beads  eleven  ap- 
pears as  one  (green)  and  ten  (red)  beads; 
twelve,  as  two  (green)  and  ten  (red)  beads ; 


so 


PRIMARY    METHODS. 


thirteen  (three-teen),  as  three  (green)  and 
ten  (red)  "beads ;  fourteen,  as  four  and  ten ; 
etc.  If  the  pupil  adds  8  +  6,  the  result, 
four  green  and  ten  reel  balls,  almost  says 
fourteen  to  him.  If  he  is  to  subtract  16  —  9, 
he  removes  with  little  trouble  the  6  (green) 
and  3  (red)  balls  as  nine.  This  advantage 
is  invaluable  in  the  formation  of  distinct 
mental  number  images,  in  accordance  with 
the  current  decimal  system  of  notation. 

I  append  a  few  series  of  typical  exercises 
within  the  limits  of  1  to  20.  The  reader 
should  study  them  with  the  help  of  a 
string-  of  beads  or  some  suitable  substitute, 
such  as  buttons  or  perforated  beans,  if  he 
would  fully  appreciate  the  value  of  the 
device.  The  mode  of  treating  them  is  in- 
dicated on  pp.  48  and  49,  Exercise  3. 


(i) 


12 
13 
18 
14 
11 


11  = 


2)             (3) 

(4)              (5)                   (6) 

1  + 

(1) 

12 

i 

1(15) 

2  + 

(2) 

14 

i 

16+   4 

3  + 

(3) 

15 

t 

9+    8 

4+       3 

(4) 

18 

+6       i 

(12)        17-    8 

5  + 

(5) 

13 

t 

16-11 

6  + 

(6) 

16 

i 

6  (3) 

7  + 

10 

f 

17  +   5 

8  + 

20 

9  + 

A    NUMERAL    FRAME    FOR    EACH    PUPIL.        SI 


12  = 


r>              (8) 

(9) 

(10) 

3  + 

11- 

6+   i(8)= 

6  +  7  +  ^(6) 

4  + 

13- 

i(9)+ll       = 

1(9)  +11 

5+           4  = 

iO 

f  (6)+    3(4)= 

8-i(15)  +  4 

20 

1C) 

f  (8)+    2(6)= 

4  +  4(4)-}(4) 

30 

JO 

16+   1(8)= 

f  (15)-i(12) 

40 
60 

ig 

For  the  sake  of  avoiding  misapprehen- 
sion, I  add  the  solutions  of  these  exercises 
as  they  would  appear  on  the  children's 
slates : 


(1) 

(2) 

(3)                          (4) 

8+5=13 

11  =  1  +  10 

3  (1)=:   3           12+6=2  (6) 

7+5=12 

11=2+    9 

3  (2)=   6           14+6=2  (6)  +  2 

9+5=14 

11=3+    8 

3  (3)=   9           15+6=2  (6)  +  3 

6+5=11 

11=4+    7 

3  (4)=12           18+6  =  3  (6) 

12+5=17 

11=5+    6 

3  (5)=15           13+6=2(6)  +  ! 

13+5=18 

11=6+    5 

3  (6)=18           16+6=2  (6)  +  4 

18+5=23 

11=7+    4 

10+6  =  1  (6)  +  4 

14  +  5  =  19 

11=8+    3 

20+6=3  (6)  +  2 

11  +  5  =  16 

11=9+    2 

(5) 

(6) 

(7)                     (8) 

1  (12)=6 

f  (15)=   9 

12=3+9        4=11-7 

t  (12)=4 

16+   4=4 

(4)          12=4  +  8        4=13-9 

|  (12)=2  (4)= 

8         9+8  =17 

12  =  5  +  7        4=    i  (8) 

i  (12)=3 

17-   8=9 

12=2  (6)       4=    i(12) 

|  (12)=3  (3)= 

9      16-11  =   5 

12  =  3  (4)       4=    t(16) 

t  (12)=  2 

6     (3)  =18 

12=4  (3)       4=    i(20) 

(12)=5  (2)=10      17n-5=3(5)  +  2     12  =  6(2) 


82  PRIMARY    METHODS. 

<9>  (10) 

6  +i  (8)=10  6  +  7+H6)       =16 

i  (9)+    11=14  f  (9)  +  ll          =17 

f  (6)+3(4)=16  8-H15H4     -  9 

f  (8) +  2  (6)=18  4+4  (4)-J  (4)=19 

16     -hi  (8)=  4  (4)  |  (15)-|  (12)  =19 


CHAPTER    VIII. 

THE  COUNTING  BLOCKS. 

tHESE    are   wooden   one-inch   "blocks,    de- 
rived  from   the    third   gift.      They   are 
used     in     three     sizes :        (1)     whole     cubes 
(Ixlxl  in.)   fjjSp,    (2)  half  cubes  (lxlx|in.) 
gjfp,   (3)  quarter  cubes    (lx£x|  in.)    J9.     For 

ordinary  number  exercises,  especially  in 
primary  work,  the  whole  cubes  are  most 
serviceable.  They  are  more  easily  handled, 
and— because  of  their  regular  shape— fit  in 
all  positions,  and  do  not  divert  the  atten- 
tion from  number  to  form.  The  half  and 
quarter  cubes  may  be  dispensed  with  alto- 
gether in  number  lessons;  at  any  rate,  they 
should  not  be  used  for  this  purpose  until 
number  images  are  well  fixed  by  the  ex- 
clusive use  of  whole  cubes. 

The  number  images  furnished  by  these 
blocks  mark  an  important  advance  in  men- 
tal growth  with  reference  to  number.  The 
balls  of  the  "numeral  frame"  touch  only 


54  PRIMARY    METHODS. 

in  one  point,  so  that  even  "beads  of  the 
same  color  retain  their  individuality  prom- 
inently in  the  twos,  threes,  fours,  fives,  etc., 
of  the  lessons ;  the  child  readily  recognizes 
in  each  two,  three,  four,  five  the  constit- 
uent two,  three,  four,  five  ones.  The  count- 
ing blocks,  on  the  other  hand,  coalesce 
quite  perfectly  on  contact ;  an  entire  face 
of  one  coincides  with  an  entire  face  of  the 
neighbor,  and  the  group  of  blocks  forms  a 
complete,  unbroken  whole.  The  modest 
division  lines  do  not  force  their  presence 
on  the  child's  attention ;  still  they  are 
sufficiently  clear  to  be  readily  distinguished, 
and  to  announce  without  difficulty  the 
number  of  constituent  ones  in  the  new 
composite  unit.  Color,  too,  is  removed  so 
that  the  pupil's  number  conceptions  are 
more  and  more  freed  from  other  phases  of 
material  existence  that  cling  to  things,  and 
brought  nearer  to  the  pure  forms  of  ab- 
stract ideas. 

Before  the  teacher  attempts  to  guide  the 
work  of  the  children,  she  should  have  ex- 
perienced these  effects  of  the  new  number 
forms  upon  her  own  mind.  For  this  pur- 
pose she  should  provide  herself  with  a 


THE     COUNTING     BLOCKS. 


sufficient  number  of  these  blocks  (a  few 
cents  will  purchase  one  hundred),  and  carry 
out  the  suggestions  of  the  following  pages 
for  herself,  extending  the  exercises  accord- 
ing to  her  own  needs.  In  the  work  of  the 
children  the  suggestions  already  made  hold 
good.  A  limited  number  of  typical  lessons 
in  counting,  analysis  and  synthesis  of  num- 
bers, and  in  the  fundamental  operations 
will,  therefore,  suffice  to  unlock  the  possi- 
bilities of  this  occupation.  In  the  diagrams 
each  square  represents  a  cube. 

I.  COUNTING  EXERCISES. 

(1)  The  child  receives  ten  or  twelve 
blocks,  and  counts  from  one  to  ten,  the 
successive  number  forms  presenting  the 
following  or  similar  phases : 


QQ 


am, 


,  &c.  to  10. 


,  &c.  to  12. 


66 


PRIMARY    METHODS. 


D. 

1  1, 

T 

> 

1  1 

| 

L  &c.  to  10. 

(2)  The  child  receives  from  eighteen  to 
twenty  blocks,  and  counts  by  twos,  threes, 
fours,  or  fives. 


*nn. 


,  &c. 


It  will  be  noticed  that  the  child  thus 
secures  a  variety  of  mobile  images  of  the 
various  numbers.  Thus  in  (a)  5  appears  as 
4  +  1,  in  (6)  as  3  +  2,  in  (c)  as  5  (1)  or  1  (5) ; 
in  (a)  and  (d)  6  appears  as  3  (2),  in  (6)  and 
(e)  as  2  (3),  in  (r)  as  5  +  1,  etc. 

II.   ANALYSIS  AND  SYNTHESIS  OF  NUMBERS. 

OO  DOmOD  OO 

20),  (1+1),  2,  (1+1),  2(1). 

It  will  be  seen  that  in  Exercise  (1),  post- 


THE    COUNTING    BLOCKS.  57 

tion  answers  a.  purpose  similar  to  that  ac- 
complished by  color  on  pp.  34-36,  with  this 
difference,  however,  that  the  position  of 
each  cube  is  in  the  pupil's  control.  In  the 
first  form,  both  cubes  are  in  the  same 
slanting-  position,  touching  only  corner  to 
corner  ;  they  appear  as  two  separate  ones 
equal  in  position,  or  as  2  (1)  ;  in  the  second 
form  they  stand  in  different  positions, 
touching  again  only  in  one  point  ;  they 
appear  as  two  separate  ones  in  different 
positions,  or  as  (1  +  1)  ;  in  the  third  posi- 
tion they  have  fully  united,  face  to  face, 
into  a  new  composite  unit  ;  they  appear  as 
a  two,  1  (2)  ;  the  fourth  and  fifth  forms  are 
repetitions  of  the  first  and  second  in  in- 
verse order,  forming  the  descending  portion 
of  a  position  -wave  similar  to  the  color 
waves  of  Chapter  V.  and  VI. 


•OOO 

8  GQ,  (14-1+1),  (2+1),  (3). 

In  this  exercise,  the  number  three  is  sim- 
ilarly treated.  We  have  successively,  three 
ones  in  the  same  position,  yet  clearly  sepa- 
rated, one  and  one  and  one,  two  and  one, 
and  one  three. 


58 


PRIMARY    METHODS. 


(3),(2+i)orCl-t- 
2,)  3  (!}.  4. 


tfb 


(Ex.  3  and  4  read  from  top  to  bottom  or 
vice  versa.  This  may  "be  done  with,  all 
these  exercises.) 


&c.  (4),  (3+ 1)., 
2  (2),  4  (1). 


However,  such  exercises  will  prove  quite 
cumbersome.  They  may  be  indulged  for 
silent  practice  to  a  limited  extent,  but  for 
class-instruction  more  efficient  modes  must 
be  found.  I  have  found  it  best,  for  this 
purpose,  to  beg-in  on  the  analytic  side  of 
the  work. 

Thus  for  Ex.  6  the  child  receives  four 
fours  (16  blocks)  arranged  at  equal  distances 
from  left  to  right.  The  task  is  to  analyze 
them  successively  in  accordance  with  the 
number  indications : 

(2  +  2)  (1  +  3)  (1  +  2  +  1)  (4  (1)).    The  results 


THE     COUNTING     BLOCKS. 


59 


indicated  in  Ex.  6  may  "be  reached  by  dic- 
tation or  "by  independent  study  on  the  part 
of  the  more  practical  children. 


Bel 


c.< 

fis 

d.- 

n  m  n 

n  n 
n  n 

For  Ex.  7  the  children  have  received  fif- 
teen "blocks  each.  The  lesson  is  indicated 
on  the  blackboard  : 

1+     =5 

2+     =  £ 

2(2)+     =  5 

Three  sets  of  answers  are  indicated  in  the 
Exercise  (7). 


n 


O 


El 


m 


60 


PRIMARY    METHODS. 


For  Ex.  8  each,  cliild  lias  received  six 
"blocks.  Trie  lesson  lias  "been  indicated  on 
the  blackboard :  1  +  =  6  ;  2  +  =  6  ;  3  +  =6; 
6+2=  ;  6-5-3  =  .  The  child  has  solved 
the  problems  successively,  and  has  recorded 
the  solutions  on  the  slate,  in  drawing  and 
writing,  and  Ex.  8  shows  one  of  the  results: 


D 


B 


1  +  5  =  6, 


2  +  4  =  6 


9BB. 


=  3(2) 


The  great  value  of  these  blocks  in  fac- 
toring deserves  special  notice.  For  this 
purpose  it  is  used  to  great  advantage  even 
in  the  fifth  grade.  Indeed,  I  have  found 
children  of  still  higher  grades  derive  real 
benefit  from  an  occasional  return  to  these 
"things,"  'when  problems  involving  factor- 
ing had  to  be  solved. 

A  few  illustrations  will  make  this  clear. 
I  have  selected  for  this  purpose  the  num- 
bers 9,  10,  15,  12,  28,  36.  For  the  number- 
forms  the  blocks  are  arranged  in  accord- 


THE    COUNTING    BLOCKS. 


61 


ance  with,  our  decimal  system  of  notation, 
so  that  the  number  of  tens  and  units  may 
be  readily  distinguished ;  thus  : 


10 


15  =  10  +  5 


=  10+2 


28  =  2  (10) +8 


36  =  3  (10) +6 


The  pupils  should  then  proceed  in  sys- 
tematic order,  testing  the  lowest  factor  first. 
Thus  (9)  would  successively  go  through  the 
following  changes : 

a.  ZK  c. 


(10)  and  (15)  are  less  refractory,  yielding 
at  once  the  forms  2  (5)  and  3  (5),  respect- 
ively : 


62 


PRIMARY    METHODS, 


15  =  3(5) 

(12)  may  pass  through  a  variety  of  suc- 
cessive transformations  ;  in  (a)  12  =  2  (6)  = 
2x2(3),  in  (6)  12  =  3  (4)  =  3  x2  (2). 


12 


3(6) 


2x2(3) 


12 


3(4) 


m    en    an 
m    an    m 

3X2(2) 

The   following   diagrams  will    sufficiently 
illustrate  the  factorings  of  (28)   and  (36). 


THE    COUNTING    BLOCKS. 


63 


In  the  illustration,  twenty-eight  is  first 
resolved  into  2  (10)  and  2  (4)  =2  (14)  ;  then, 
in  twice  two  sevens  [2x2  (7)]. 

For  thirty-six,  two  factorings  are  given 
on  p.  64.  In  the  first  of  these,  "bisection  ar- 
ranges the  number  in  2  (10)  +  2  (5)  +  2  (3) 
=  2  (18).  These,  "by  a  second  bisection,  are 
readily  grouped,  each,  in  2  (9),  reducing  36 
to  2  x  2  (9).  Lastly,  the  trisection  of  the 
nines  yields  four  sets  of  three  threes,  or 
2x2x3  (3). 

The  same  process  is  somewhat  simplified 
in  the  second  illustration  of  the  reduction 
of  thirty-six.  We  see  successively  two  sets 
of  two  nines,  2x2  (9),  and  two  sets  of  twice 
three  sets  of  three,  2x2x3  (3). 


28 


2  (14)       = 


2X2  (7). 


64 


PRIMARY    METHODS. 


36 


2  (18)      = 


2  X  2  (9) 


2  X  2  X  3  (3) 


36 


&c. 


2  X  2  (9) 


irm 


2X2X3  (3). 


CHAPTER   IX. 

THE    COUNTING    BLOCKS.      (Concluded.) 

Q-o 

tN  tlie  use  of  the  blocks  for  the  funda- 
mental operations — addition,  subtraction, 
multiplication,  division,  and  part-taking- — 
the  number-forms  should  be  constructed  in 
accordance  with  our  decimal  system  of  no- 
tation. Sixteen  should  appear  clearly  as 
one  ten  and  one  six;  twenty-six  as  two 
tens  and  one  six,  etc.  I  have  found  it  most 
convenient  for  this  purpose  to  lay  under 
each  other  as  many  tens  (rows  of  ten  blocks) 
as  the  number  indicates,  and  the  number 
of  units  under  these.  (See  p.  61,  where  the 
number-forms  of  9,  10,  15,  12,  28,  and  36 
are  shown.) 

In  the  solutions  of  problems  it  is  best  to 
dispose  first  of  the  tens  of  the  number  to 
be  added  or  subtracted.  Thus,  if  27  is  to 
be  added,  add  first  the  20  and  then  the  7 ; 
if  39  is  to  be  subtracted,  subtract  first  the 
30  and  then  the  9 ;  if  4  (26)  is  the  prob- 


66  PRIMARY    METHODS. 

lem,  find  4  (20)  and  4  (6),  etc.  This  is  in 
strict  accordance  with  the  number-names 
above  20 ;  language  says  :  Add  twenty-seven, 
subtract  thirty-nine,  find  the  value  of  four 
twenty-sixes,  etc.  Besides  this  mode  of  pro- 
cedure by  removing-  the  bulkiest  portion  of 
the  task  first,  facilitates  mental  processes, 
and  enables  the  pupils  to  ride  safe  between 
the  Scylla  of  verbalism  and  the  Chary bdis 
of  slavish  subjection  to  slate-work. 

In  the  following  pages  I  present  the  suc- 
cessive number-forms  as  they  occur  in  the 
solutions  of  a  number  of  problems,  illustrat- 
ing the  use  of  the  blocks  in  the  various  fun- 
damental operations.  To  these  I  have  added 
a  few  examples  of  involution  in  connection 
with  the  finding  of  areas  and  volumes. 

I.  ADDITION  : 

TYPICAL  PROBLEMS  : 

1.  8  +  5=  3.    14  +  5=  5.    14  +  7  = 

2.  9  +  6=  4.    11  +  7=  6.    19  +  5  = 

7.  24+15=  9.   29  +  23  = 

8.  26  +  14=  10.   26  +  27= 

SPECIMEN  SOLUTIONS  : 
'8  +  5    = 


13 


THE    COUNTING    BLOCKS. 


67 


15 


4-  6      = 


14 


+  5     «= 


8. 


19 


14 


21 


.19 


+ 


24 


24 


15     = 


68 


PRIMARY    METHODS. 
29  +  23 


=  29+20  f  3         = 


52 


II.   SUBTRACTION  ; 

TYPICAL  PROBLEMS  : 

1.  16-4=  3.   28-12  = 

2.  12-7-  4.   32-26  = 

SPECIMEN  SOLUTIONS 
16  —4  = 


5.  58-34= 

6.  51-29  = 


12 


i 

itzn 

12 


-7 


THE    COUNTING    BLOCKS. 


69 


28 


_      12      =  16 

I 1 1— r — 7 — , — T— y — | r 

!        !  !        !        !  ! 


3 


3 

3 

26 

=  6 

T  ]   T 

r~r~r~T"T"T"i 

....p-  p-j— 

i 

...i..i._,.J 

j  — 

32—30-  2-  <=6. 

III.   MULTIPLICATION: 

SPECIMEN  SOLUTIONS  : 

1.    4  (9)  =  2  (18)  =  2  (10)  +  2  (8)  =  36. 


&c. 


g.    3(13)  =  3  (10)  +  3  (3)  =  39; 


&c. 


70 


PRIMARY    METHODS. 


8.    0  (4)  =  3  (12)  =  3  (10)  +  3  (2)  =  36. 


m 
en 
m, 


IV.  DIVISION  : 


SPECIMEN  SOLUTIONS  : 


1.    24 -+-3  =  8  (3). 


I   1 

I  i 

(The  four  blocks  on  the  right  are  moved  to  the  lowest  row; 
in  the  second  form  the  threes  may  he  slightly  separated  from 
left  to  right.) 

2.    28  -•-  2  =  10  (21  +  4  (2)  =  14  (2). 


BBBB0BBBBB 


m  m  m 


THE    COUNTING    BLOCKS. 


71 


V.  PART-TAKING: 

SPECIMEN  SOLUTIONS: 


%  (25)  [« (25)  =  5]  ^3  (5)  -15. 


VI.   INVOLUTION 


2*=  4 


3!=9 


4J=16 


n 
r~H 


5*=  25 


72 


PRIMARY    METHODS. 


6*=  36 


3'= 


CHAPTER     X. 

THE     FOLDING     SHEET. 

the  exercises  to  be  suggested  under 
this  head,  paper  sheets  of  various  sizes 
and  shapes  may  be  provided.  The  most 
convenient  for  class  use  are  squares  of  four 
inches  to  the  side,  equilateral  triangles  of 
four  inches  to  the  side,  and  circles  four 
inches  in  diameter.  For  drawing,  I  have 
found  a  fair  quality  of  unsized  manilla 
wrapping  paper  quite  suitable ;  although, 
for  some  purposes,  a  good  quality  of  un- 
sized printing  paper  may  be  preferred.  The 
same  sheets  will  answer  for  geometrical 
exercises ;  nevertheless,  for  reasons  to  be 
stated  hereafter,  colored  unglazed  cover- 
paper  will  be  found  more  satisfactory  and 
not  very  expensive.  The  square  and  tri- 
angular paper  can  be  cut  cheaply  on  a 
cutting-machine  by  the  nearest  book-binder 
or  job-printer.  The  circular  papers  will 


74  PRIMARY    METHODS. 

have  to  be  ordered  from  the  manufacturer, 
or  cut  to  order  "by  the  children. 

In  folding,  stress  should  "be  laid  on  ac- 
curacy, care,  and  cleanliness ;  the  creases 
should  be  sharply  defined  "by  drawing-  the 
back  of  the  thumb-nail  firmly  over  the 
folds.  In  the  dictation  exercises,  the  pupils 
should  not  change  the  position  of  the  paper 
unless  by  direction,  and  should  not  lift  the 
paper  from  the  table  until  the  desired  form 
is  completed.  I  shall  show,  first,  how  the 
sheets  may  be  prepared  and  used  for  draw- 
ing exercises,  and  then,  how  they  may  be 
used  in  form  lessons. 

I.   THE  SQUAEE  SHEET  IN  DRAWING. 

For  an  introductory  exercise,  the  pupil 
should  study  the  form  features  of  the  sheet 
before  him ;  he  should  count  and  describe 
the  edges,  corners,  and  angles. — ["  One  edge 
in  front  (or  below),  one  edge  behind  (or 
above),  one  edge  on  the  right,  one  edge  on 
the  left." — "The  front  (lower)  edge  and  right 
edge  form  a  corner — the  right  front  (lower) 
corner;  the  front  edge  and  left  edge  form  a 
corner — the  left  front  (upper)  corner;"  etc.— 
'•  The  front  (lower)  edge  and  back  (upper) 


THE    FOLDING     SHEET.  76 

*• 

edge  run  from  right  to  left ; "  etc. — "  The 
rig-lit  and  left  edges  are  in  the  same  direc- 
tion (from  front  to  hack)  or  parallel;  the 
front  and  hack  edges  are  in  the  same  di- 
rection (from  right  to  left)  or  parallel." — 
"The  left  edge  makes  a  right  angle  "with  the 
front  edge, — the  left  edge  is  perpendicular  to 
the  front  edge, — the  front  edge  is  perpen- 
dicular to  the  left  edge, — the  left  and  front 
edges  are  perpendicular  to  each  other,"  etc. — 
"The  lower  and  upper  edges  are  horizontal, 
the  right  and  left  edges  are  vertical" — Place 
the  fore-finger  of  the  left  hand  on  the 
front  edge, — the  fore-finger  of  the  right 
hand  on  the  edge  parallel  to  this,  on  an 
edge  perpendicular  to  it,  on  the  opposite 
edge,  on  an  adjacent  edge,  etc. — Place  the  fore- 
fingers on  the  edges,  forming  the  left  front 
corner,  the  left  hack  corner,  etc.]  In  all 
these  exercises  the  technical  terms — itali- 
cized above — should  "be  freely  used. 

For  the  first  exercises  in  drawing,  the 
paper  is  prepared  as  follows,  the  teacher 
dictating:  "Place  the  sheet  before  you  with 
two  edges  running  from  right  to  left,  and 
two  from  front  to  back. — Place  the  right 
edge  on  the  left  edge,  and  crease  the  paper 


76  PRIMARY    METHODS. 

in  tlie  fold.— Open  the  paper*.— Front  edge 
on  "back  edge;  crease;  openf. — Right  edge  oil 
vertical  diameter  (or  crease) ;  crease ;  open. 
Left  edge  on  vertical  diameter;  crease; 
open.  Front  edge  on  horizontal  diameter; 
crease ;  open.  Back  edge  on  horizontal  diam- 
eter; crease;  open.J 

The  thirty-five  suggestive  figures  of  the 
subjoined  plate  indicate  how,  "with  the  help 
of  the  sheet  creased  into  sixteen  square 
inches,  as  the  above  dictation  teaches,  the 
teacher  may  secure  automatism  in  drawing- 
straight  lines,  parallel  and  diverging,  in  all 
directions.  Similar  series  can  easily  "be 

*  The  folio-wing  facts  may  here  be  fixed  in  lively  conversa- 
tion -with  the  children:  "The  vertical  crease  passes  through  the 
middle  of  the  paper ;  it  is  a  diameter  of  the  square  ;  it  cuts  the 
paper  into  two  equal  oblongs ;  each  oblong  is  the  half  of  the 
square ;  the  vertical  diameter  bisects  the  square  ;  it  bisects  the 
front  edge ;  it  bisects  the  back  edge ;  it  is  parallel  to  the  right 
and  left  edges;  perpendicular  to  the  front  and  back  edges,"  etc. 

t  Here  facts  like  these  may  be  brought  out  in  conversation : 
"The  horizontal  diameter  bisects  the  right  and  left  edges;  it 
bisects  the  vertical  diameter ;  the  two  diameters  bisect  each 
other ;  the  two  diameters  cross  at  the  center  of  the  square ;  they 
divide  the  sheet  into  four  equal  squares,"  etc. 

$  Here  the  fact  that  the  paper  is  divided  into  smaller  squares 
may  be  noticed,  and  the  squares  counted. — "How  many  rows  of 
squares  from  right  to  left ;  how  many  from  front  to  back ;  how 
many  squares  in  each  row;  how  many  in  the  paper?"  — The 
number  of  creases,  their  relative  directions,  the  angles  which 
they  form,  and  other  things  may  be  noticed  and  distinctly  an- 
nounced by  the  children  in  full,  clear  sentences,  until  they  are 
quite  familiar  with  the  paper  and  love  it  for  the  pleasure  ob- 
tained from  it. 


THE    FOLDING     SHEET. 


77 


constructed  by  the  teacher  for  the  practice 
of  curved  lines,  although,  for  this  purpose, 
other  appliances  are  preferable. 


78 


PRIMARY     METHODS. 


II.    THE  EQUILATERAL  TRIANGLE  IN  DRAWING. 

Here  again,  for  an  introductory  exercise, 
the  pupil  may  study  the  form  features  of 
the  triangle — the  position  of  its  edges  and 
corners,  the  equality  of  its  sides  and  angles. 
The  sheet  may  then  be  prepared  for  draw- 
ing, as  follows  :  "  Place  the  sheet  "before  you, 
one  edge  in  front  from  right  to  left,  the 
other  two  slanting  backward.  Place  the 
right  (slanting)  edge  on  the  left  (slanting) 
edge,  and  crease  the  paper  in  the  middle- 
— Open  the  paper.  *  Front  edge  on  left 
slanting  edge, — crease, — open. — Front  edge  on 
right  slanting  edge, — crease,— open."— (In  Fig. 
1  of  the  plate  of  suggestive  figures  on  the 
next  page,  the  resulting  creases  are  indi- 
cated by  the  lines  c  d,  a  e,  5 /.)f— "Place  the 


*  Here  the  folio-wing  facts  may  be  brought  out:  "The  crease 
lies  from  front  to  back  ;  it  bisects  the  front  edge  ;  it  bisects  the 
triangle ;  it  bisects  the  back  angle ;  it  is  perpendicular  to  the 
front  edge  ;  it  cuts  the  triangle  into  two  equal,  right,  scalene 
triangles." 

t  Here  it  may  be  noticed  that  the   three   creases   (or   altitudes) 


THE     FOLDING     SHEET. 


79 


back  corner  on  the  middle  of  front  edge, 
— crease, — open  ; — right  corner  on  the  middle 
of  left  edge, — crease, — open  ; — left  corner  on 
the  middle  of  right  edge, — crease, — open."- 
(In  Fig.  1,  the  creases  are  shown,  "by  the 
lines  e  /,  e  d,  f  d.)* 


intersect  at  a  common,  point,  the  center  of  the  triangle,  that  they 
divide  the  triangle  into  six  equal,  right,  scalene  triangles  ;  that 
the  two  triangles  in  front  (on  the  right,  on  the  left)  form  an 
isosceles,  obtuse  triangle ;  that  the  two  triangles  in  the  right 
(left,  back)  corner  form  a  trapezium,  etc. 

*  Here  it  may  be  noticed  that  the  three  short  creases  divide 
the  equilateral  triangle  into  four  smaller  equal  equilateral  tri- 
angles ;  that  the  short  create  from  right  to  left  (/  <?)  is  parallel 
to  the  front  edge,  and  divides  the  sheet  into  a  trapezoid  and  a 
small  equilateral  triangle,  etc. 


80 


PRIMARY    METHODS. 


III.    THE  CIRCULAR  SHEET  IN  DRAWING. 

The  sheet  is  prepared  as  follows  (Fig.  1, 
in  the  plate  on  the  next  page) :  Front  half 
on  hack  half, — crease, — open  (ad)*  ; — right  half 
on  left  half  (or  right  end  of  diameter  on  left 
end), — crease, — open  (cd) ;  f — right  quadrant  in 
front  on  left  quadrant  "behind, — crease, — open 
(gh) ; — left  quadrant  in  front  on  right  quad- 
rant hehind, — crease, — open  (ef). 

For    the   suggestive    Figs.   8-14,   each  half 


*  Facts  to  be  brought  out  in  conversation  :  The  crease  ab  bi- 
sects the  circle;  it  bisects  the  circumference;  each  half  of  the 
circle  is  called  a  semicircle ;  the  crease  is  a  diameter. 

t  Pacts  to  be  brought  out :  The  two  diameters  bisect  each 
other ;  they  cross  at  the  cenier  of  the  circle ;  they  divide  the 
circle  into  four  equal  parts ;  each  of  these  parts  is  a  quadrant. 


THE    FOLDING    SHEET. 


81 


quadrant  is  again  "bisected  by  an  additional 
crease. — For  Figs.  15,  16,  17,  the  front  and 
back  ends  of  tne  diameter  cd  (lying  from 
front  to  back),  and  the  right  and  left  ends 
of  the  diameter  ab  are  successively  folded 
on  the  center,  giving  chords  parallel  to 
these  diameters.  For  Figs.  18-21,  each 
semicircle  is  trisected,  and  in  Fig.  21  each 
sextant  is  subsequently  bisected. 


82  PRIMARY     METHODS. 

17. 


18. 


19. 


21. 


20. 


CHAPTER     XI. 

THE   FOLDING   SHEET   (Concluded). 

tN  the  annotations  of  the  previous  chap- 
ter, I  have  indicated  to  some  extent 
how,  in  the  preparation  of  the  drawing- 
sheets,  rudimentary  notions  on  form  and 
direction  may  he  hrought  out  and  fixed. 
In  the  present  chapter,  I  shall  suggest  ex- 
ercises which  are  very  serviceable  in  more 
or  less  systematic  lessons  on  form. 

I.    THE  SQUARE  SHEET  IN  FORM  LESSONS. 


84 


PRIMARY    METHODS. 


9. 


10. 


THE    FOLDING    SHEET. 


83 


30. 


A  square  sheet  of  paper  may  be  laid  "be- 
fore each  child.  Simple  observation  will 
"bring  out  in  oral  or  written  -work,  series  of 
facts  or  statements  like  the  following,  suit- 
able for  various  stages  of  progress  :  (a)  "  The 
paper  is  square.  It  has  four  sides.  It  has 
four  corners.  It  has  four  right  angles." — 
(Z>)  "  The  right  side  of  the  square  is  parallel 
to  the  left  side ;  the  lower  side  is  parallel 
to  the  upper  side.  The  right  side  is  per- 
pendicular to  the  upper  (and  lower)  side ; 
the  left  side  is  perpendicular  to  the  upper 
(and  lower)  side,  etc.  The  opposite  sides  are 
parallel ;  the  opposite  sides  are  equal.  The 
adjacent  sides  are  parallel  (equal)."  (c)  "The 
square  has  four  sides ;  it  is  a  quadrilateral. 


86  PRIMARY    METHODS. 

Its  opposite  sides  are  parallel ;  it  is  a  par- 
allelogram. Its  sides  are  equal ;  it  is  an 
equilateral  parallelogram.  Its  angles  are 
right ;  it  is  a  right  parallelogram.  It  is  a 
right,  equilateral  parallelogram." 

The  children  may  be  requested  to  fold 
the  lower  side  on  the  upper  one,  to  crease 
and  open  (Fig.  1  of  the  above  table) : 
"  The  crease  bisects  the  square ;  it  bisects 
the  right  (left)  side.  It  is  a  diameter.  This 
diameter  is  horizontal.  It  is  perpendicular 
to  the  right  (left)  side.  It  is  parallel  to  the 
upper  (lower)  side." 

Similarly  the  children  may  study,  in 
Fig.  2,  the  oblong;  in  Fig.  3,  the  vertical 
diameter;  in  Fig.  4,  another  oblong;  in 
Fig.  5,  the  two  diameters ;  in  Fig.  6,  one 
diagonal ;  in  Fig.  7,  the  right  isosceles  tri- 
angle ;  in  Fig.  8,  both  diagonals,  etc.  In 
the  figures  the  blank  spaces  inclosed  by 
clotted  lines  show  the  portion  of  the  paper 
folded  on  the  hatched  part  of  the  figure. 

For  Fig.  9  (trapezoid),  after  creasing  a 
diagonal,  the  lower  side  is  folded  on  the 
diagonal.  The  subsequent  folding  of  the 
left  side  on  the  same  diagonal,  gives  the 
trapezium,  Fig.  10.  From  this  we  obtain 


THE    FOLDING     SHEET.  87 

Fig.  11  by  folding  the  riglit  isosceles  tri- 
angle of  Fig.  10  inward.  Fig.  12  (scalene 
obtuse  triangle)  comes  from  Fig.  10  by 
folding  the  lower  half  upon  the  upper  half 
of  the  trapezium.  Fig.  13  (rhomboid)  comes 
from  Fig.  9  by  folding  the  upper  side  upon 
the  diagonal.  From  this  Figs.  14,  15,  16, 
and  17  are  easily  derived. 

For  Fig.  18,  the  child  has  been  directed 
to  open  the  last  fold  of  Fig.  17,  and  to  turn 
the  lozenge  over.  On  the  reverse  side,  the 
two  diagonals  will  be  distinctly  observed, 
and  the  child  may  be  taught  to  see  and 
say:  "The  long  diagonal  bisects  the  short 
one.  The  short  diagonal  bisects  the  long 
one.  The  two  diagonals  bisect  each  other. 
The  short  diagonal  is  perpendicular  to  the 
long  one.  The  two  diagonals  are  perpen- 
dicular to  each  other,"  etc. 

The  remaining  figures  (19-31)  suggest  ex- 
ercises in  the  social  synthesis  of  the  forms 
obtained.  Thus,  for  Fig.  19,  four  children 
have  placed  together  the  right  isosceles  tri- 
angles obtained  by  folding  Fig.  7,  so  as  to 
inclose  a  slanting  hollow  square.  Other 
combinations  of  the  same  form  are  shown 
in  Figs.  20  and  21.  Similarly,  Figs.  22,  23, 


88 


PRIMARY    METHODS. 


and  25  show  combinations  of  the  trapezium 
(Fig.  10);  Figs.  24  and  26,  of  the  isosceles 
triangle  (Fig.  11);  and  Figs.  27-31,  of  the 
lozenge  (Fig.  15). 

The  designs  may  he  pinned  to  the  wall 
or  pasted  on  manilla  paper,  and  thus  util- 
ized in  ornamenting  the  school-room  and 
as  patterns  for  drawing  or  coloring. 

II.    THE  EQUILATERAL  TRIANGLE  IN  FORM  LESSONS. 

After  -what  has  been  said  concerning  the 
square  sheet,  little  need  he  added  in  ex- 
planation of  the  following  cuts : 


THE    FOLDING     SHEET. 


89 


In  Fig".  1  the  cliilcl  studies  tlie  equilateral' 
triangle  as  such  and,  after  folding1  the  right 
half  upon  the  left  and  opening  the  paper, 
the  relation  of  the  altitude  to  the  triangle. 
In  Fig.  2,  he  studies  the  three  altitudes ;  in 
Fig.  3,  a  right  scalene  triangle  (half  of  the 
equilateral) ;  in  Fig.  4,  a  trapezoid ;  in  Fig. 
5,  a  lozenge;  in  Fig.  6,  a  new  smaller  equi- 
lateral ;  in  Fig1.  7,  after  opening  all  the 
folds,  the  relations  of  parts.  Figs.  8-11  show 
the  growth  of  the  hexag-on ;  and  Figs.  12-14 
give  some  additional  hints,  on  the  basis  of 
the  net-work  obtained  in  the  last  series  of 
foldings,  concerning  a  new  line  of  drawing- 
and  coloring-  designs. 

III.    THE  CIRCULAR  SHEET  IN  FORM  LESSONS. 


90 


PRIMARY    METHODS. 

8. 


Fig.  1  represents  the  sheet  re-opened  after 
the  creasing-  of  the  horizontal  diameter; 
Fig.  2,  the  same  after  the  creasing  of  two 
perpendicular  diameters ;  Fig.  3,  the  semi- 
circle; Fig.  4,  a  quadrant;  Fig.  5,  parallel 
chords;  Fig.  6,  segments;  Fig.  7,  the  in- 
scribed square.  Figs.  8-12,  suggest  social 
syntheses. 

These  suggestions  must   suffice.     For   the 


THE    FOLDING     SHEET.  91 

thoughtful  teaclier  they  will  open  many 
avenues  to  rich  fields  of  investigation  on 
the  subject  of  form,  in  many  grades  of  the 
school.  To  her,  however,  as  in  previous 
cases,  I  must  leave  the  task  of  selecting  and 
adapting  the  exercises  and  of  preparing  the 
details  of  each  lesson. 

In  all  folding  exercises  it  is  essential  for 
permanent  success  to  secure  neatness  and 
promptness ;  neatness  first  and  foremost,  and 
then  promptness.  K~ever,  under  any  circum- 
stances, sacrifice  the  former  to  the  latter. 
For  this  purpose,  it  is  well  strictly  to  observe 
a  few  rules,  even  at  the  risk  of  some  ped- 
antry : 

1.  Insist  that  all  folding  and  creasing  be 
done  on  the  table ;  never  allow  the  children 
to  lift  up  the  paper  and  do  the  folding  and 
creasing  in  the  air. 

2.  Insist   that   the  paper  be  kept  in   the 
same  position   during   the   entire    dictation, 
not  turned  so  as  to  bring  the  right  side  in 
front  when   the    direction   is   given   to   fold 
from  right  to  left,   etc. 

3.  Insist  that  point  shall  lie  accurately  on 
point  and  edge  on  edge,  before  any  creasing 
is  attempted. 


92  PRIMARY     METHODS. 

4.  Insist  that  the  creasing-  be  clone  slowly 
and     deliberately    with.1    the     back     of    the 
thumb-nail    or    some    suitable    instrument, 
such  as  a  paper-knife. 

5.  Insist  that  the  creasing  be  done  thor- 
oughly, so  that  the  folds  may  lie  flat. 

6.  Insist   that    in    opening   the    folds    the 
child  keep  the  paper  smooth  and  avoid   all 
crumpling. 

7.  Dictate  slowly,  deliberately,  with  ample 
pauses,  avoiding  nervous  repetition. 


CHAPTER    XII. 

PLASTIC     CLAY. 

Cfci 

fN  very  many  localities  this  material  may 
be  had  for  the  digging-.  Elsewhere  it 
may  be  procured  from  potteries  at  rates 
varying  from  £  to  3  cents  per  pound.  It 
may  be  broken  up  in  a  pail,  moistened  with 
water,  worked  into  suitable  consistency, 
wrapped  in  a  moist  cloth,  covered  with  an 
oil  cloth,  and  laid  aside  for  use.  When 
ready  for  "work  the  teacher  may  slice  off 
pieces  of  suitable  size  with  -  a  piece  of 
copper  wire  of  convenient  length.  Each 
child  is  furnished  with  a  modeling  board 
about  one  foot  square,  which  will  be  cut 
to  order  at  the  planing-mill  for  five  or  six 
cents  a  piece,  and  with  a  modeling  knife 
which  may  be  bought  at  25  cents  per  dozen 
or  whittled  out  of  soft  wood  by  the  boys. 
The  knives  should  be  six  inches  long,  the 


94  PRIMARY    METHODS. 

blade  three  fourths  to  one    inch  wide,   of  a 
shape  indicated  by  the  following  cut : 


In  fashioning  the  clay,  the  children  use 
only  gentle  pressure  "with  the  thumbs  and 
fingers.  Violent  pressure  and  beating  are 
as  inexpedient  as  they  are  unseemly.  For 
smoothing,  after  the  fingers  have  done  their 
best,  the  blade  of  the  knife  is  drawn  gently 
over  the  surface  with  a  minimum  of  press- 
ure. For  trimming  the  edges  and  carving, 
the  knife  blade  is  used  like  that  of  an  or- 
dinary knife.  For  engraving  designs  on.  the 
surface  of  the  clay,  the  point  of  the  handle 
is  used.  On  account  of  the  softness  of  the 
surface,  gentleness  and  delicacy  of  touch 
are  imperative.  Thus  the  work  with  clay 
becomes  an  excellent  corrective  of  the  in- 
jurious influences  of  slate-work  upon  the 
hand,  as  well  as  an  excellent  school  of 
patient,  thoughtful  persistence. 

The  easiest  and  most  fertile  work  for 
primary  grades,  with  endless  resources  for 
the  exercise  of  inventive  power  and  manual 
skill,  lies  in  the  manufacture  of  tiles  of 


PLASTIC    CLAY.  95 

various  shapes ;  in  succession  of  difficulty, — 
square,  circular,  octagonal,  hexagonal,  tri- 
angular (equilateral),  pentagonal.  With, 
children  who  have  not  enjoyed  the  advan- 
tages of  kindergarten  training,  the  first  few 
lessons  should  "be  devoted  to  free  random 
exercises  or  play  with  the  clay.  They  may 
he  allowed  to  make  marbles,  cakes,  loaves 
of  "bread,  birds'-nests,  and  "birds,  snakes,  and 
hundreds  of  other  things  according  to  their 
fancy.  This  "will  render  them  familiar  with 
the  plastic  properties  of  the  material,  and 
will  thoroughly  arouse  their  interest.  Dur- 
ing these  play-lessons,  too,  the  need  of 
gentleness  in  handling  the  clay  should  be 
inculcated ;  the  children  will  soon  learn 
that  easy,  delicate  treatment  yields  better 
results. 

For  the  manufacture  of  the  square  tile, 
each  child  receives  about  two  cubic  inches 
of  clay.  By  gentle  pressure  with  the  fingers, 
this  is  spread  out  on  the  modeling  'board 
in  a  flat  cake,  about  4£  inches  square,  and 
not  quite  one  fourth  inch  thick.  The  sur- 
face of  this  is  scraped  smooth  with  the  clay 
knife,  and  the  edges  are  trimmed  so  as  to 
leave  a  smooth  tile,  four  inches  square.  The 


96 


PRIMARY    METHODS. 


teacher,  in  passing  from  child  to  child, 
giving  directions,  helping,  and  encourag- 
ing (or  one  of  the  children  appointed  for 
this  purpose),  is  constantly  busy  picking 
up  from  the  "boards  scraps  of  clay ;  this  will 
insure  neatness  and  respect  for  the  material. 
With  the  help  of  the  ruler  and  the 
pointed  knife-handle,  or  some  other  suitable 
style,  the  children  may  then  analyze  the 
surface  in  a  variety  of  "ways,  reaching  more 
or  less  complicated  net-works  for  guidance 
in  exercises  of  engraving,  carving,  or  paint- 
ing. The  following  figures  indicate  the 
principal  ones  of  these  net-works.  The 
figures  on  page  77,  Chapter  X.,  suggest  ex- 
ercises for  drawing  or  engraving.  Exercises 
for  carving  and  coloring  will  readily  sug- 
gest themselves  to  a  thoughtful  considera- 
tion of  the  net- works.  In  Figs.  12,  13,  and 
14,  the  net-works  appear  as  little  picture- 
frames  to  be  filled  according  to  the  child's 
taste  'and  skill. 


PLASTIC    CLAY. 


97 


10. 


In  the  manufacture  of  the  circular  tile 
the  child  proceeds  as  above.  When  the  tile 
is  ready  for  trimming-,  he  may  stick  a  stout 
pin  near  the  center  of  the  tile,  tie  another 
pin  to  a  piece  of  thread  about  ten  inches 
long,  pass  this  thread  around  the  central 
pin  so  as  to  obtain  a  radius  of  four  inches, 
and  with  the  free  pin  mark  the  circum- 
ference of  the  circle  on  the  tile.  The  ex- 
cess of  clay  is  then  trimmed  off  with  the 
clay-knife,,  and  the  tile  is  ready  for  work 
in  accordance  -with  previous  suggestions, 
and  on  the  basis  of  net-works,  indicated1 
below. 

15.  16.  17.  18.  19. 


98 


PRIMARY    METHODS. 


20. 


The  circular  tiles  offer  convenient  sur- 
faces for  practice  with  dividers  in  the 
drawing-  of  circles  and  circular  arcs,  as  in- 
dicated in  the  following  cuts.  One  of  the 
points  of  the  dividers  may  "be  protected 
•with  a  small  disc  of  card-board  to  keep  it 
from  penetrating-  too  far  into  the  plastic 
clay.  In  the  place  of  dividers,  two  pins 
and  a  thread,  as  above,  will  answer  the 
purpose.  The  following  figures  suggest  some 

29.  30.  81. 


PLASTIC    CLAY.  99 

such,  exercises.  The  various  fields  may  be 
painted  in  different  colors  to  make  the 
forms  more  impressive  and  to  please  the 
children. 

In  the  making  of  solid  forms,  similar 
directions  hold  good.  The  pupils  should, 
again,  rely  chiefly  on  gentle  pressure  with, 
the  thumbs  and  fingers ;  all  beating  and 
hammering  should  be  discountenanced.  For 
purposes  of  smoothing  and  decorating  the 
faces  of  ttie  solids,  the  same  instruments 
and  expedients  are  used  as  in  the  making 
of  tiles.  The  fashioning  of  the  solids  offers 
excellent  opportunities  for  the  education  of 
the  sense  of  touch  with  reference  to  shape. 
Much  is  gained  in  this  direction  by  re- 
questing the  children  frequently  to  close 
their  eyes  while  going  through  the  initial 
processes  of  coaxing  the  clay  into  the  re- 
quired shape.  This  will  not  only  add  a 
new  interest  to  the  exercise,  but  will  help 
to  clear  the  children's  notions  of  shape,  by 
inducing  them  to  concentrate  their  atten- 
tion on  the  sense  of  touch  as  the  true 
shape  sense.  In  all  cases,  much  heed  should 
be  given  to  efficient  means  for  interesting 
the  child  in  the  shapes  under  considera- 


1OO  PRIMARY    METHODS. 

tion.  These  means  are  found  chiefly  in  the 
decoration  of  the  pure  shapes,  and  in  their 
modification  and  combination  for  imitating 
objects.  The  various  shapes  are  "best  con- 
sidered in  the  following-  order : 

(1)  Cube ;  Square  Prism ;  Square  Pyramid. 

(2)  Cylinder;    Prisms  of  three,  six,   eight, 
five  sides. 

(3)  Cone;    Pyramids    of  three,    six,    eight, 
five  sides. 

(4)  Sphere;    Spheroids;    Tetrahedron    and 
Octahedron. 

The  teacher's  tact  and  opportunities  must 
decide  to  what  extent  each  of  these  shapes 
can  be  used  in  the  study  of  objects  and  of 
geometrical  relations,  as  well  as  in  drawing 
and  coloring.  In  my  experience  I  have 
found  them  of  great  value  in  all  grades  of 
the  Primary  and  Grammar  Departments. 


CHAPTER    XIII. 

CUTTING     AND     MOUNTING. 

tHE  materials  for  this  occupation  are  the 
square,  circular,  and  triangular  folding- 
sheets  and  suitable  paper  or  card-board  for 
mounting.  For  the  latter  purpose,  stout 
manilla  wrapping-  paper,  cut  in  pieces  seven 
to  nine  inches  square,  is  quite  serviceable. 
A  pair  of  cheap  blunt-pointed  scissors,  a 
small  dish  or  bottle  with  mucilage,  a  small 
clean  piece  of  cotton  cloth,  and  a  camel- 
hair  brusli  complete  the  outfit. 

The  simplest  and,  for  primary  school  use, 
the  most  efficient  method  of  preparing-  the 
square  sheet,  is  indicated  in  the  following 
dictation:  "Lay  the  sheet  before  you,  the 
front  (nearest)  side  from  right  to  left ;  lay 
the  front  edge  on  the  back  edge,  crease  in 
the  fold,  open  the  paper ;  the  right  on  the 
left  edge,  crease,  open ;  the  front  edge  on 
the  middle  (horizontal)  crease  (diameter), 
crease,  open ;  the  b'ack  on  the  horizontal 


1O2  PRIMARY    METHODS. 

diameter,  crease,  open ;  the  right  on  the 
vertical  diameter,  crease,  open ;  the  left 
on  the  vertical  diameter,  crease,  open." 
(These  creases  divide  the  sheet  into  sixteen 
square  inches,  Fig-.  1.)  "Fold  the  front 
edge  again  on  the  "back  edge ;  the  left  (short) 
edge  on  the  right  (short)  edge." 

The  paper  is  now  ready  for  "work  (Fig.  2). 
The  point  c  indicates  the  center  of  the 
original  large  square  sheet ;  the  dotted  lines 
show  the  creases  which  serve  as  guides  in 
cutting.  In  the  subsequent  figures  (3-19), 
the  heavy  lines  indicate  the  cuts.  Thus, 
in  Fig.  3,  the  left  and  lower  margins  are 
marked  heavy.  The  paper  is  cut  in  these 
lines,  and  thus  divided  into  four  smaller 
squares  of  four  square  inches  each,  which 
may  he  arranged  in  a  variety  of  new  ways 
and  mounted  on  a  suitable  sheet  of  paper 
or  card-board,  or  used  as  rudimentary  exer- 
cises in  mensuration. 

In  the  following  cut,  Figs.  3-15  suggest  a 
number  of  rectilinear  cuts;  Figs.  16-19,  a 
few  combinations  of  rectilinear  -with  cir- 
cular cuts;  and  Figs.  31-36,  two  cuts  di- 
verging from  the  center,  combined  with 
other  available  cuts. 


CUTTING     AND     MOUNTING. 


103 


1O4 


PRIMARY     METHODS. 


Fig's.  20,  21,  and  22  show  three  arrange- 
ments (or  syntheses)  made  with  the  pieces 
resulting-  from  the  cut  (analysis)  indicated 
in  Fig.  4. 

For  the  arrangement  of  Fig.  23,  two 
children  who  had  sheets  of  different  colors, 
have  exchanged  the  squares.  If  one  of  these 
had  a  blue,  and  the  other  a  yellow  sheet, 
Fig.  23  would,  then,  represent  a  square 


CUTTING    AND    MOUNTING.  1OS 

• 

made  up  of  a  "blue  (yellow)  cross,  with  a 
yellow  (blue)  square  laid  in  eacli  corner. 
In  the  figure,  the  difference  in  color  is  in- 
dicated "by  the  different  directions  of  the 
hatching  lines.  The  same  device  has  "been 
used  for  a  similar  purpose  in  Figs.  25,  28, 
30,  38,  and  40. 

Fig.  24  is  a  re-arrangement  of  the  pieces 
obtained  from  Fig.  11. 

Fig.  25  is  a  reconstruction  of  the  square, 
after  an  exchange  of  forms  among  three 
children ;  perhaps  the  large  central  square 
is  "blue,  the  small  triangles  red,  and  the 
small  squares  in  the  corners  yellow.  The 
other  two  children  will,  then,  have  similar 
reconstructions  with  the  same  colors  in 
different  arrangements. 

Figs.  26,  27,  and  28  are  obtained  from  the 
cuts  of  Fig.  15  ;  Figs.  29  and  30,  from  the 
cuts  of  Fig.  17;  Figs.  37  and  38,  from  the 
cuts  of  Fig.  32 ;  and  Figs.  39  and  40,  from 
the  cuts  of  Fig.  36. 

It  is  scarcely  needful  to  point  out  the 
ample  opportunities  which  these  exercises 
offer,  for  the  varied  and  interesting  use  of 
geometric  language,  and  for  the  cultivation 
of  the  esthetic  sense  with  reference  to 


1O6 


PRIMARY     METHODS. 


form  and  color ;  to  speak  of  the  certainty 
with  which  a  thoughtful  use  of  this  charm- 
ing work  will  lead  the  child  to  important 
discoveries  concerning  the  laws  of  the 
equality,  similarity,  and  equivalence  of  fig- 
ures ;  or  to  indicate  how  much  these  ex- 
ercises will  aid  the  child  in  the  work  of 
drawing  and  coloring. 

After  these  explanations,  very  little  need 
be    added    in    elucidation    of    the    subjoined 

* 

cut,  suggesting  the  treatment  of  the  cir- 
cular sheet. 

1.  2.  3. 


• 


4.  5.  6.  7.  8.  9.  10. 


11.  12.  13.  14.  15.  16.  17. 


18.  19.  20.  21.  22.  23.  24. 


25. 


26. 


27. 


CUTTING    AND    MOUNTING. 


107 


28. 


Figs.    1,    2,    and    3    represent  the   circular 
sheet,  respectively,  (1)  laid  oefore  the  pupil, 

(2)  the  lower  half  folded  on  the  upper  half, 

(3)  the  left  half  on  the  right  half.    In  Figs. 
4  to  27,  the  heavy  lines   indicate   the    cuts 
to    he    made    on   the    quadrants.      Figs.    28, 
29,    and    30,    suggest    arrangements    of    the 
pieces    from    the    cuts    of    Fig.    5  ;    Fig.     31 
comes  from  Fig.   11  ;    Figs.  32   and  33,   from 
Fig.    16;   Fig.   34,  from  Fig.    23. 

.For  the  use  of  the  equilateral  triangle 
(four-inch  side),  the  follov-nng-  cut  will  give 
the  needed  directions. 


1O8 


PRIMARY    METHODS. 


CUTTING    AND    MOUNTING.  1O9 

Figs.  1-6  indicate  the  successive  steps  in 
the  preparation  of  the  sheet  for  cutting1, 
a,  5,  c  mark  the  vertices  of  the  triangle ; 
n,  o,  r,  the  middle  of  the  sides ;  ra,  the  cen- 
ter of  the  triangle.  The  dictation  may  take 
the  following  form :  Lay  the  triangle  before 
you,  one  side  in  front,  from  right  to  left 
(Fig.  1) ;  lay  the  left  slanting  side  (ca)  on 
the  right  slanting  side  (cb),  and  crease  the 
paper  in  the  fold  (en)  (Fig.  2) ;  lay  the  "back 
point  (c)  on  the  right  point  in  front  (ba) 
(Fig.  3) ;  move  the  "back  part  of  the  paper 
to  the  right,  and  lay  the  right  side  from 
front  to  hack  (Fig.  4) ;  turn  the  paper  over 
forward  (Fig.  5) ;  lay  the  left  (slanting)  side 
on  the  right  (vertical)  side  (Fig.  6).  The 
sheet  is  now  ready ;  the  vertices  of  the 
triangle  are  all  in  the  same  point  (cab),  the 
middle  points  of  the  sides  in  orn,  and  the 
center  of  the  sheet  in  m. 

Figs.  7-21  indicate  simple  rectilinear  cuts, 
bisecting  sides  and  yielding  a  great  variety 
of  geometrical  forms  for  exercises  similar 
to  those  suggested  in  the  treatment  of  the 
square  and  circular  sheets.  Figs.  22-28  sug- 
gest a  few  curvilinear  cuts. 

The    subjoined    foldings    of    the    square 


1  10 


PRIMARY     METHODS. 


sheet,  given  in  kindergarten  manuals,  I 
have  not  found  as  available  in  primary 
work  as  those  just  treated,  which  have  the 
advantage  of  greater  simplicity  in  prepara- 
tion and  in  the  forms  resulting-  from  the 

cuts. 

i. 


CUTTING    AND    MOUNTING.  Ill 


/ 

0 

V 

bd 

Fig.  1  shows  the  square  folding  sheet  in 
position,  "  one  corner  in  front  and  all  sides 
slanting";  for  Fig.  2  the  left  corner  a  has 
been  placed  on  the  right  corner  c,  and  the 
paper  creased  from  d  to  6;  for  Fig.  3  the 
back  corner  d  has  been  placed  on  the  front 
corner  b,  and  the  paper  creased  from  m 
to  ca ;  for  Fig.  4 ,  the  corner  or  point  d 
has  been  lifted  from  b  and  folded  on  ca, 
bringing  the  points  cad  together ;  Fig.  5 
shows  the  form  turned  over  backward  in 
order  to  bring  the  point  b  to  the  top ;  for 
Fig.  6  the  point  b  is  folded  on  the  points 
acb,  and  the  paper  creased  from  m  to  rost. 
This  unites  all  the  corners  or  angles  of  the 
square  in  the  one  point  dacb,  all  the  middle 
points  of  the  sides  of  the  square  in  the 
point  rost,  and  exposes  the  center  of  the 
square  at  the  point  m.  The  folding  sheet 
is  now  ready  for  such  cuts  as  the  teacher 
or  pupil  may  devise,  and  all  cuts  will  pro- 
duce symmetrical  results. 


112  PRIMARY    METHODS. 

Fig.  7  shows  the  first  fold  of  a  second 
series  starting  from  the  position  of  Fig.  1  ; 
for  Fig.  8,  the  left  point  (a)  -was  laid  on  the 
right  (c),  and  the  paper  slightly  creased  at 
the  point  m ;  for  the  fold  of  Fig.  9,  the 
angle  at  m  should  span  120°;  in  Fig.  10, 
the  angle  at  m  is  60°;  for  Fig.  11,  the  paper 
is  turned  over  from  left  to  right;  the  por- 
tion "below  the  line  ef  is  clipped  off,  and  the 
form  is  ready  for  work. 


CHAPTER    XIV. 

CARD-BOARD  WORK. 

tHE  cheapest  and  most  satisfactory  ma- 
terial for  card-board  work  is  a  stout 
manilla  board,  which  the  printer  or  binder 
may  cut  of  the  required  sizes, — usually  from 
six  to  twelve  inches  square.  A  pencil,  a 
ruler,  a  pair  of  dividers,  a  sharp  knife,  some 
pieces  of  clean  paper,  a  little  mucilage,  and 
a  cutting-board,  twelve  inches  square,  com- 
plete the  outfit.  For  the  sake  of  securing 
a  fair  amount  of  skill  in  the  treatment  of 
the  material  and  the  use  of  the  tools,  the 
pupils 'may  first  practice,  in  a  few  lessons, 
the  drawing  and  cutting  out  of  given  num- 
bers of  figures  of  given  forms  and  dimen- 
sions. Tasks  like  the  following  may  be  set : 

(1)  Draw   and    cut   out    six   squares,   2x2 
inches. 

(2)  Draw  and  cut  out  six  equilateral  tri- 
angles, each  side  two  inches  long. 


114 


PRIMARY    METHODS. 


(3)  Draw  and  cut  out  six  hexagons,  each 
side  two  inches  long. 

(4)  Draw  and  cut  out  six  pentagons,  from 
circles  of  two  inches  diameter. 

(5)  Draw  and  cut  out  six  two-inch  squares, 
and  "bisect  them  into  two  triangles. 

(6)  Draw  and  cut  out  six  equilateral  tri- 
angles (two  inches  to  the  side),   and  trisect 
each  into  three  triangles. 

The  pieces  resulting  from  the  solutions 
of  these  tasks  should  toe  re-arranged  sym- 
metrically toy  the  pupils,  and  the  resulting 
forms  and  angles  stiidied.  The  following 
figures  suggest  some  of  these  arrangements 
for  the  first  two  tasks :  Figs.  1  and  2,  for 
the  first ;  Figs.  3  and  4,  for  the  second ; 
Fig.  5,  for  tooth  comtoined. 

The   forms    thus    ototainecl   offer   elements 


3. 


CARD-BOARD     WORK. 
5. 


115 


4. 


for  designs  in  drawing,  and  furnish  themes 
for  form  lessons  for  all  grades  of  primary 
and  grammar  schools. 

Next,  in  point  of  difficulty,  would  be  a 
series  of  exercises  in  making  hollow  forms 
or  "boxes."  Some  of  these  forms  are  sug- 
gested in  the  following  figures,  on  the  bases, 
successively,  of  the  square,  oblong,  equilat- 
eral triangle,  lozenge,  and  hexagon : 


2. 


116 


PRIMARY    METHODS. 


a  w??"i 


The  outline  is  first  carefully  drawn  on 
the  card-board ;  this  gives  opportunity  for 
practice  in  the  use  of  instruments  for  geo- 
metrical drawing.  The  dotted  lines  (shown 
in  a  of  each  pair  of  figures)  is  then  cut 
half  through  the  paper  with  the  help  of  a 
ruler  and  a  sharp  knife ;  this  enables  the 
pupil  subsequently  to  fold  the  sides  of  the 
boxes  upward,  as  shown  in  &  of  each  pair 


CARD-BOARD    WORK.  117 

of  figures.  Fig1.  2  represents  the  shape  of 
small  pieces  of  paper  or  "  binding  slips," 
cut  of  the  required  length  for  binding  the 
faces  at  the  edge  of  the  boxes.  The  middle 
line  represents  a  crease  ;  this  is  placed  ex- 
actly over  and  along  the  edge,  and  each 
half  of  the  ""binding  slip"  is  firmly  pasted 
on  the  two  adjacent  faces  forming  the 
edge.  For  the  box  (6)  in  Fig.  1,  eight  such 
slips  of  equal  length  would  be  required, 
four  for  the  sides,  and  four  for  the  bottom 
and  sides ;  for  the  box  of  Fig.  2  it  would 
be  necessary  to  prepare  six  slips  of  one 
length  and  two  of  doube  that  length,  etc. 
The  last  step,  the  manufacture  of  solid 
forms,  offers  now  little  difficulty.  Figs.  8, 
9,  and  10  show  that  by  the  addition  of  one 
surface  the  box  forms  1,  3,  and  4  are  changed 
into  solids,  a  cube  and  two  square  prisms. 
A  little  patience  and  care  will  overcome 
the  slight  difficulty  of  fastening  the  lid  or 
sixth  surface.  Figs.  11,  12,  and  13  show 
the  way  to  the  construction  of  the  trian- 
gular prism,  the  square  pyramid,  and  the 
regular  tetrahedron.  Figs.  14,  15,  and  16 
give  the  net-work  for  the  regular  octahe- 
dron, icosahedron,  and  dodecahedron. 


118 


PRIMARY    METHODS. 


By  substituting1,  for  the  triangles  4  and  5 
in  Fig.  11,  hexagons,  octagons,  or  pentagons, 
and  adding  the  required  numbers  of  rect- 
angles (three,  five,  or  two,  respectively)  the 
six-sided,  eight-sided,  or  five-sided  prisms 
•will  he  obtained.  By  similar  changes  in 
Fig.  12,  corresponding  pyramids  will  result.; 
8.  9. 


CARD-BOARD    WORK. 


119 


It  is  evident,  without  further  explana- 
tion, that  these  forms  may  "be  used  profit- 
ably in  all  grades  of  primary  and  grammar 
schools  for  a  variety  of  exercises  in  rudi- 
mentary form  lessons,  mensuration,  draw- 
ing, and  solid  geometry. 

It  is  evident,  too,  that  "where  circum- 
stances permit,  the  pupils  may  from  the 
same  material,  with  little  difficulty,  fashion 
models  of  pieces  of  furniture,  buildings,  and 
a  number  of  objects  for  purposes  of  draw- 
ing; and  that  geometrical  analysis  and  syn- 
thesis will  find  the  material  serviceable  at 
every  step. 


120  PRIMARY    METHODS. 

In  all  cases,  it  is  desirable  to  give  direc- 
tions in  few  words,  setting  a  clearly  denned 
task  on  the  "basis  of  which  the  pupil  may 
do  the  work  independently.  He  should 
first  assure  himself  of  the  correctness  of 
his  solution  by  carefully  drawing  the  out- 
line of  the  cuts  on  a  piece  of  paper,  as  in 
Figs.  8,  9,  10,  11,  12,  13,  14,  15,  and  16. 
Subsequently  the  drawing  should  be  trans- 
ferred to  the  manilla  board,  and  the  work 
may  then  proceed  as  indicated  above. 


CHAPTER    XV. 

FRACTION   STRIPS. 

NY  kind  of  strong,  thin,  -well  calen- 
dered paper  will  answer  the  purposes 
of  these  strips.  The  children,  however,  will 
be  "best  pleased  with  strips  cut  from  tinted 
cover  paper  or  "engine-colored"  paper.  The 
paper  may  be  bought  by  the  quire  or  ream, 
and  cut  to  order  by  the  printer  or  binder. 
For  use  in  numbers,  as  "fraction  strips" 
proper,  they  should  be  one  half  or  (later) 
one  third  inch. 'wide,  and  twenty  or  twenty- 
four  inches  long.  For  use  in  form  lessons, 
as  intertwining  strips,  they  should  be  one 
inch  wide. 

In  forming  the  first  definite  notions  of 
fractions,  the  child  should  have  objects 
which  he  can  actually  break  up  into  parts 
of  one,  in  such  a  way  that  the  parts  can 
readily  be  re-arranged  in  the  order  of  the 
original  whole,  or  of  new  wholes  dictated  by 
the  teacher  or  invented  by  the  child.  To 


122  PRIMARY    METHODS. 

this,  in  the  limits  of  |  to  -j^,  the  fraction 
strips  are  well  adapted. 

For  a  first  exercise  with  halves,  the  fol- 
lowing is  suggested :  Place  a  (twenty-inch) 
strip  before  you  from  left  to  right.  Lay 
the  right  half  on  the  left  half;  crease  the 
strip  in  the  fold ;  open  the  strip  (Fig.  1) ; 
carefully  tear  the  strip  in  the  crease. — Lay 
one  half  from  left  to  right ;  lay  the  other 
half  parallel  to  the  first  one  inch  (two, 
three,  etc.,  inches)  in  front  ("behind)  it. — Lay 
one  half  from  front  to  back ;  lay  the  other 
half  parallel  to  the  first  one  inch  (two, 
three,  etc.,  inches)  to  the  right  (left)  of 
the  first ;  and  so  on  through  a  variety  of 
relative  positions,  as  indicated  in  Figs.  2 
to  8. 

In  each  of  these  re-arrangements  the  child 
recognizes  a  new  unit  in  which  the  two 
halves  unite  more  or  less  completely  into 
a  whole.  The  child's  attention  may  "be  di- 
rected to  this  cautiously  and  without  ur- 
gency ;  in  no  case,  however,  should  the 
growth  of  the  ideas  —  one  whole  is  two 
halves,  two  halves  are  one  whole — be  inter- 
rupted by  premature  formal  statements  or 
by  abstract  philosophizing  thereon. 


FRACTION     STRIPS. 


123 


J 


Oj 


b.l 


13. 


16. 


PI 


LJ 


m 
~j 


_J 


PRIMARY    METHODS 


24. 


25. 


ill 

For  the  exercise  with,  one  fourth,  sug- 
gested in  Figs.  9-14,  attention  should  "be 
paid  to  the  colors  of  the  strips :  the  three 
strips,  a,  &,  c,  in  Fig.  9,  should  "be  of  dif- 
ferent colors.  These  color  contrasts  will 
make  the  fraction  contrasts  more  impress- 
ive. 

In  Figs.  15,  16,  and  17,  exercises  for  still 
further  contrasting  halves  and  fourths  are 
suggested.  In  Fig.  15,  the  equivalence  of 


FRACTION    STRIPS.  125 

one  (red)  half  and  two  (blue)  fourths  is 
quite  prominent. 

Fig.  18  contrasts  thirds,  halves,  and 
fourths,  and  Figs.  19-25  suggest  re-arrange- 
ments of  thirds. 

Dictations  are  quite  helpful  here  in  bring- 
ing numerical  relations  into  prominence. 
Thus,  for  Fig.  11:  "Lay  two  fourths  par- 
allel from  right  to  left,  five  inches  apart ; 
lay  the  other  two  fourths  between  their 
ends,  from  front  to  back,  five  inches  apart, 
making  a  square." — This  dictation  contains 
and  conveys  the  formula  f  +  f  =  1.  The 
same  formula  lies  in  Fig.  14. 

In  Figs.  12  and  13,  lies  the  formula  J  +  i  =  l. 

Figs.  20-25,  by  the  similar  positions  (par- 
allel or  diverging)  of  two  thirds  and  the 
clear  contrast  in  position  of  the  remaining 
third,  say  clearly  f  +  %  =  1. 

These  hints  will  suffice  to  show  the  edu- 
cational value  of  the  fraction  strip,  and  to 
enable  the  reader  to  use  it  effectively,  in 
the  limits  indicated  above,  in  the  develop- 
ment of  clear  notions  concerning  the  re- 
lations of  fractions  to  the  whole  and  to 
each  other. 

The    wide   (one    inch)    fraction  strip,    pre- 


126  PRIMARY    METHODS. 

pared  as  an  intertwining-  strip,  will  be  found 
very  serviceable  in  the  development  of  ideas 
of  position  and  form.  More  particularly  for 
the  former,  I  have  found  it  invaluable.  It 
is  prepared  as  follows  :  "Lay  the  strip  before 
you  from  right  to  left  (Fig.  a),  fold  the 
upper  third,  lengthwise,  on  the  remainder 
of  the  strip,  and  crease  carefully  in  the 
fold  (Fig.  6) ;  fold  the  front  third  length- 
wise on  the  upper  third  and  crease  care- 
fully in  the  fold  (Fig.  c). 


It  may  be  necessary  to  assist  a  number 
of  children  the  first  time  in  making  these 
somewhat  difficult  long  creases ;  but  they 
will  find  the  work  easy  and  enjoyable  after 
this. 

For  exercises  in  positions,  the  children, 
by  dictation,  hold  the  strips  well  stretched 
between  their  hands,  "  horizontal,  vertical, 
slanting  (to  the  right,  left,  back,  etc.),  par- 
allel to  the  front  edge  of  the  desk,  perpen- 


FRACTION    STRIPS.  127 

dicular  and  oblique  to  it  (or  to  some  otlier 
line  or  plane),  from  North  to  South,  from 
East  to  West,"  etc.  The  interest  of  exercises 
in  relative  positions  will  be  still  further 
increased,  if  children  are  grouped  in  sets  of 
two,  one  of  whom  has  a  red  and  the  part- 
ner a  yellow  strip  (other  color  contrasts 
will  answer  the  same  purpose).  The  red 
(or  yellow)  strips  are  then,  by  dictation, 
held  parallel,  perpendicular,  oblique  to  the 
yellow  (or  red)  strips,  at  a  variety  of  dis- 
tances, points,  and  angles. 

The  subjoined  figures  (1-7)  may  suffice  to 
indicate  how  the  intertwining  strips  may 
be  used  for  exercises  with  angles  (right,  ob- 
tuse, and  acute),  as  well  as  for  the  making 
of  given  geometrical  forms.  At  the  points, 
marked  m,  one  end  of  the  strip  is  inserted 
between  the  folds  of  the  other  end. 

Thus  Fig.  1  is  a  right  angle  which,  by 
dictation,  may  be  held  in  a  variety  of  posi- 
tions, or  may  be  united  with  the  right 
angles  of  neighbors  into  a  variety  of  forms. 
Or,  it  may  be  used  to  represent  a  carpen- 
ter's square,  the  letter  L,  a  tent,  etc.  Fig. 
2  is  a  square,  a  picture-frame,  a  window,  an 
inclosed  well,  etc. 


123 


PRIMARY    METHODS. 


7/1 


CHAPTER    XVI. 

SPLINTS  OR  STICKS. 

QUARE  match,  splints,  cut  of  the  re- 
quired lengths,  offer  a  remarkably 
cheap  and  serviceable  material  for  form  and 
number  studies,  as  well  as  for  drawing-  ex- 
ercises. They  can  be  had  from  dealers  in 
lengths  of  one  to  five  inches.  Where  this 
is  impracticable,  pieces  of  straw,  strips  of 
card-board,  or  tooth-picks,  appropriately  cut, 
will  answer  the  purpose  quite  -well. 

In  a  short  chapter,  it  is  possible  only  to 
indicate  the  wealth  and  flexibility  of  this 
material  in  school  work.  For  this  purpose, 
a  few  typical  lessons  have  been  sketched 
below.  The  first  series  is  devoted  to  lessons 
in  the  rudiments  of  form. 


3.. 


ISO  PRIMARY    METHODS. 


h.H 


•(. 

Jnl_ 


9. 


10. 


11. 


13. 


12. 


SPLINTS    OR    STICKS. 


131 


15. 


16. 


Figs.  1-4  indicate  exercises  for  position, 
actual  or  symbolic  (as  in  drawing-  from 
objects).  Each,  child  receives  a  supply  (9-12) 
of  splints,  four  inches  long,  with  which  he 
works,  at  first  "by  dictation,  and  afterward 
independently,  as  follows  (Fig.  1) : 

"Lay  six  sticks  near  your  right  hand, 
and  six  sticks  near  your  left  hand.— With 
the  right  hand,  lay  one  stick  (eight  inches 
behind  the  edge  of  the  desk)  from  right  to 
left. — With  the  left  hand  lay  one  stick  one 
inch  to  the  left  of  this,  from  front  to  back ; 


132  PRIMARY    METHODS. 

with,  the  right  hand,  lay  a  third  stick  from 
front  to  "back,  one  inch  to  the  right  of  the 
first  stick."  Questions  may  now  be  asked, 
to  fix  the  contrasted  ideas :  "  How  many 
sticks  from  front  to  hack  ?  from  right  to 
left  ?  Where  is  the  stick  from  right  to 
left  ?  Where  are  the  sticks  from  front  to 
back  ? "  The  •  children  may  then  be  per- 
mitted to  make  a  number  of  similar  "  forms  " 
or  "drawings"  with  the  remaining  sticks; 
and,  subsequently,  to  imitate  these  on  the 
slate,  the  paper,  or  the  blackboard. 

Or  we  may  dictate  as  follows  (Fig.  2) : 
"  I  see "  (the  children  laying  on  the  desks 
the  forms  described)  "  nine  inches  from  the 
desk  front,  near  the  middle  of  the  desk,  a 
straight  line  from  right  to  left ;  right  and 
left  of  this  I  see  two  straight  lines  slant- 
ing inward  and  backward." 

Or  (Fig.  4),  using  the  symbolic  terms, 
horizontal  for  "from  right  to  left,"  vertical 
for  "from  front  to  back,"  etc. — we  may  say: 
"Draw  with  one  stick,  near  the  middle  of 
the  desk,  a  vertical  line ;  draw  right  and 
left  of  the  vertical  two  horizontal  lines ; 
draw  right  and  left  of  these  lines  slanting 
inward  at  the  top." 


SPLINTS    OR    STICKS.  133 

Similarly,  Fig.  5  teach.es  parallelism  in 
different  positions ;  Fig-.  6,  the  perpendicular 
relation  in  a  variety  of  positions ;  Fig.  7, 
the  right  angle;  Fig.  8  contrasts  right  ob- 
tuse and  acute  angles;  Fig.  12  right  arid 
acute  angles;  Figs.  9,  10,  11,  13  present 
studies  of  the  square  in  varieties  of  shape 
and  position ;  Fig.  14  contrasts  the  square 
and  lozenge;  Fig.  15,  the  square  and  oblong 
rectangle ;  Fig.  16,  the  lozenge  and  oblong 
rectangle. 

It  is  scarcely  necessary  to  add  that  in 
these  and  similar  ways  the  child  may  learn 
to  control  the  form  relations  of  all  the 
various  polygons,  and  to  apply  the  knowl- 
edge obtained  in  drawing  and  other  pur- 
suits. This  is  partly  indicated  in  the  fol- 
lowing nine  "  star  forms  : " 


134  PRIMARY    METHODS. 

30,  21. 


SPLINTS    OR    STICKS.  135 

Figs.  17,  18,  and  19  apply  the  trapezium; 
Fig-.  20,  the  lozenge ;  Fig.  21,  the  rhomboid, 
square,  and  trapezium;  Fig.  22,  the  trape- 
zium, square,  rhomboid,  lozenge,  and  dodec- 
agon;  Fig.  23,  trapezium  with  hexagon 
and  dodecagon,  etc.  Star-forms  and  other 
symmetrical  forms  may  thus  be  "drawn 
with  the  splints,"  and,  subsequently,  on 
slate  or  paper. 

Similar  devices  will  help  the  children  to 
gain  self-confidence  even  in  object-drawing, 
inasmuch  as  even  moderate  skill  will  find 
it  easy  to  lay  or  "draw  with  splints"  skel- 
eton sketches  of  houses,  barns,  fences, 
trees,  pieces  of  furniture,  etc.  My  "  Primary 
Helps"  contains  an  abundance  of  hints  in 
this  direction. 

Teachers  will  find  match  splints  very 
useful,  too,  in  the  rudiments  of  arithmetic. 
The  analysis  and  synthesis  of  numbers,  ad- 
dition, subtraction,  multiplication,  division, 
and  part-taking  are  performed  readily  in 
an  endless  variety  of  interesting  exercises 
with  the  help  of  splints.  For  such  exer- 
cises I  have  found  the  two-inch  splint  most 
convenient,  although  others  may  be  used 
profitably  enough.  The  following  cut  sug- 


136 


PRIMARY    METHODS. 


gests  a  simple  mode  of  using  these  for  ex- 
ercises in  the  limits  of  1-10. 

i. 


2. 


3. 


In  the  first  series  (Series  1)  the  number 
three  comes  to  the  child,  successively,  as 
three  ones,  two  and  one,  one  and  two,  one 
three.  In  the  first  figure  of  the  series,  the 
three  sticks  lie  in  the  same  direction  at  great 
one-inch  intervals ;  to  the  child  nothing 
unites  them,  they  are  distinctly  three  ones. 
In  the  second  figure  of  the  series,  the  upper 
two  sticks  are  more  closely  associated  as  a 
pair  or  a  two  "by  their  greater  closeness.  In 


SPLINTS     OR    STICKS. 


137 


the  tliird  figure,  this  association  of  the  two 
is  strengthened  or  intensified  "by  the  addi- 
tional uniting  contrast  of  position.  In  the 
last  figure,  the  three  sticks  are  closely  as- 
sociated in  a  three,  "one  three,"  by  the  tri- 
angle they  inclose. . 

Similar  considerations  will  reveal  in  Series 
2  the  following  number-readings  for  the 
little  learner  :  4  (1)  =  4,  2  (2)  =  4,  1  +  3  =  4, 
2  +  2  =  4,  2  +  2  (1)  =  4,  4  =  4.— In  Series  3  we 
have  :  6  (1),  2  (3),  3  (2),  2  (2)  +  1  (2),  and  3  (2) 
more  closely  associated  into  a  six  with,  the 
help  of  the  inclosed  triangle. — In  Series  4 
we  have :  7  (1),  2  (2)  +  1  (3),  or  (with  the  help 
of  previous  knowledge),  4  +  3,  2  (2)  +  1  (3), 
2(3)  +  1,  2(1) +  5,  4+3. 

By  making  bundles  of  sticks,  ten  in  each, 
similar  exercises  may  be  contrived  for  work 
within  even  higher  limits  (1-100). 

A  very  profitable  combination  of  form 
and  number  exercises  is  illustrated  in  the 
following  figures : 


v 


A 


138 


PRIMARY    METHODS. 


19. 


20. 


N/ 


A 


Figs.  1-5  show  the  four  sticks,  numeric- 
ally, as  4,  2  (2),  3  +  1,  3  +  1,  3  +  1.  As  sug- 
gestions for  form  concepts  and  drawing 
exercises,  they  represent  to  the  child,  suc- 
cessively, a  "box  or  picture,  a  house  or  shed, 
a  trowel  or  spade,  a  chair,  a  table.  The 
remainder  of  the  table  treats  the  numbers 
five,  six,  etc.,  in  a  similar  way. 


CHAPTER    XVII. 

STICKS    AND    PEAS. 

'OR  this  occupation  the  ordinary  match 
splints  may  be  sharpened  at  the  ends, 
or  a  special  kind  of  sticks  about  the  thick- 
ness of  stout  broom-straws  may  be  procured 
from  a  dealer  in  kindergarten  goods.  *  Dried 
peas,  soaked  over  night  in  water,  serve  as 
a  cement  to  bind  these  sticks  together.  If 
the  forms  are  to  be  made  more  permanent, 
the  ends  of  the  sticks  may  be  dipped  in 
mucilage  before  insertion  into  the  peas. 
For  advanced  children,  small  pellets  of 
bees-wax  about  the  size  of  peas  answer  an 
excellent  purpose. 

It  will  be  seen  from  an  examination  of 
the  illustrations  given  below  that  the  peas 
represent  points,  and  the  lines  mark  the 
distances  between  them ;  also  that  the  sur- 
faces inclosed  by  these  lines — as  well  as  the 


*  These  thin  sticks   come   five    and   ten  inches   long,    and   may 
be  cut  with  scissors  of  any  required  length  within   these  limits. 


14O 


PRIMARY    METHODS. 


solids  inclosed  "by  the  surfaces — represent 
comparatively  pure  form-concepts  quite  free 
from  any  admixture  of  materialness. 

The  cuts  show  the  growth  and  analysis 
of  the  square,  the  growth  and  study  of  the 
cube,  the  bisection  and  trisection  of  the 
right  angle,  'the  test  of  the  latter  with  the 
help  of  the  equilateral  triangle  and  hexagon, 
and  a  few  typical  regular  solids  or  crystal 
forms. 


i. 


2. 


QC 


O— — O Q 


STICKS    AND    PEAS. 
10.  11. 


141 


a 


19. 
I 


12 

' 


h 


14. 


'V* 

-01) 


142 


PRIMARY    METHODS. 


For  Fig.  1 — a  straight  line — the  pupils 
hold  the  stick  "between  thumb  and  fore- 
finger of  the  right  hand,  quite  near  the 
left  end  of  the  stick,  and  insert  the  point 
of  the  latter  in  the  pea,  held  "between 
thumb  and  forefinger  of  the  left  hand.  The 
same  is  done  on  the  right  end  of  the  stick, 
the  latter  being  held  between  the  thumb 
and  forefinger  of  the  left  hand,  and  the 
pea  in  the  right  hand. 

For  Fig.  2 — two  lines,  forming  a  right 
angle— the  stick  ab  is  held  -with  the  left 
hand,  the  pea  &  being  specially  supported, 


STICKS    AND    PEAS.  143 

and  the  stick  ~bc  is  inserted  with  the  right 
hand.  For  Fig.  3,  the  hands  change  office. 

For  Fig.  4— the  square — Fig.  2  is  laid  to 
the  right  and  in  front  of  Fig.  3  ;  the  free 
end  c  of  Fig.  2  is  inserted  in  pea  c  of  Fig. 
3,  and  the  free  end  a  of  Fig.  3  is  inserted 
in  the  pea  a  of  Fig.  2. 

Fig.  5  shows  the  first  step  in  the  anal- 
ysis of  the  square,  the  "drawing"  of  a 
diagonal ;  Fig.  6,  the  separation  toy  the 
diagonal  into  two  equal,  right,  isosceles 
triangles. — In  Fig.  7  the  two  diagonals  are 
drawn.  (For  this  purpose  four  sticks  of  the 
length  of  half. a  diagonal  may  be  used,  all 
inserted  in  the  pea  at  the  center;  or  a  pea 
may  he  slipped  to  the  middle  of  the  first 
whole  diagonal,  and  the  second  diagonal  may 
"be  made  from  two  halves.) — In  Fig.  7  the 
square  is  "broken  up  toy  the  two  diagonals 
into  four  equal,  right,  isosceles  triangles. — 
Fig.  9  indicates  a  first  step  for  analyzing 
the  square  toy  two  diameters. 

For  the  cutoe,  two  squares  are  made  (abed 
in  Fig.  10) ;  in  the  two  ends  of  one  side  of 
each  of  these,  perpendiculars  (de  and  cf)  are 
inserted ;  one  of  these  forms  is  then  in- 
verted, "bringing  the  square  to  the  top,  and 


144  PRIMARY    METHODS. 

the  perpendiculars  forward. ;  this  is  lifted 
over  and  in  front  of  trie  other,  and  the 
cube  (Fig1.  12)  completed. 

Fig.  13  shows  the  insertion  of  an  axis  of 
the  cube.  The  diagonals  in  the  upper  and 
lower  faces  simply  furnish  points  of  support 
for  the  axis. 

Figs.  14-17  illustrate  exercises  for  bi- 
secting the  right  angle.  In  Fig.  14,  the 
right  angle  is  established  on  both  sides  of 
the  stick  dc ;  in  Fig.  15,  it  is  bisected  on 
the  right  by  stick  df,  on  the  left  by  stick 
de\  in  Fig.  16,  the  removal  of  the  stick  dc 
reveals  the  right  angle  formed  by  the  bi- 
secting sticks  df  and  de;  in  Fig.  IT,  the 
removal  of  df  brings  out  the  contrast  be- 
tween the  miter  (45°)  and  the  sum  of  the 
right  angle  and  miter  (135°). 

Fig.  18  shows  the  trisection  of  the  right 
angle  on  the  two  sides  of  the  perpendicular 
dc.  In  Fig.  19,  the  removal  of  alternate 
sticks  gives  three  angles  of  60°.  In  Fig. 
20,  this  is  verified  by  the  insertion  of  sticks 
of  the  same  length  between  the  outer  or 
free  ends  of  the  radiating  sticks.  If  the 
trisection  is  correct,  this  -will  give  three 
equilateral  triangles  or  one  half  of  the  hex- 


STICKS    AND    PEAS.  143 

agon,  completed  in  Fig.  21. — Similarly  treated, 
Fig.  15  will  yield  an  octagon,  and  Fig.  18 
a  dodecagon. 

The  "building  of  the  octahedron  (Fig.  22) 
begins  with  the  laying  of  the  square.  On 
each  side  of  this  four  equilateral  triangles 
are  erected,  meeting  in  the  common  points 
o  and  r.  Fig.  23  solves  an  interesting 
"puzzle,"  the  "building  of  the  octahedron  in 
the  cube ;  the  diagonals  laid  across  the  sides 
of  the  square  merely  hold  the  peas  or  "wax 
pellets  that  represent  the  corners  of  the 
octahedron.  Fig.  24  shows  the  tetrahedron, 
"bounded  "by  four  equilateral  triangles ;  the 
six-sided  pyramid  and  the  six-sided  prism. 
Similarly  other  forms  may  "be  treated. 

These  skeleton  models  or  outlines  of  forms 
may  he  used  very  profitably  in  the  study 
of  form  and  in  drawing,  more  particularly 
in  all  kinds  of  perspective  drawing.  In  the 
study  of  the  propositions  and  problems  of 
plane  and  solid  geometry,  as  well  as  in  the 
study  of  the  rudiments  of  crystallography, 
the  sticks  and  wax  pellets  furnish,  even  in 
advanced  classes,  a  more  convenient  and 
more  efficient  aid  than  the  drawing  surface 
of  paper  or  blackboard. 


146  PRIMARY    METHODS. 

Whenever  dictation  is  used  in  these  ex- 
ercises, it  is  essential  for  orderly  success 
that  the  children  should  arrange  their 
material  similarly  (e.  g.  the  sticks  to  be 
used  on  the  right  side  of  the  table  or  desk, 
and  the  peas  in  a  neat  paper  "box  or  other 
receptacle  on  the  left  side ) ;  and  that  all 
the  -work  be  done  strictly  in  accordance 
•with  the  teacher's  directions,  slowly  and 
deliberately.  On  the  other  'hand,  full  free- 
dom in  handling-  the  material  should  be 
granted  in  independent  work. 


CHAPTER   XVIII. 

LENTILS   OR   DOTS. 

MONG  us  the  lentil  seed  is  rarely 
planted.  It  is  quite  largely  imported, 
however,  by  German  grocers,  who  sell  it  at 
very  reasonable  rates.  Froebel  found  in 
this  flat,  smooth,  circular  seed  a  most  serv- 
iceable representative  of  the  point  or  posi- 
tion, as  I  shall  show  directly.  Other  seeds 
have  been  proposed  —  such  as  beans,  peas, 
wheat,  barley,  etc. — but  had  to  be  aban- 
doned as  inadequate.  Mrs.  Hailmann,  there- 
fore, contrived  an  artificial  lentil  seed,  a 
circular  disk,  one  fourth  inch  in  diameter, 
cut  from  wood.  These  are  furnished  white, 
black,  and  in  the  rainbow  colors,  by  Mr. 
Bradley,  at  low  rates.  For  primary  work, 
too,  he  furnishes  similar  disks  cut  from 
gummed  paper,  which  are  of  great  value  in 
form  and  color  exercises,  and  cost  very 
little.  The  subjoined  plate  will  suggest  the 
manner  in  which  this  most  flexible  material 


148 


PRIMARY    METHODS. 


may  be  used  in  lessons  on  form.  For  this 
purpose  I  have  cliosen  a  somewhat  system- 
atic treatment  of  the  square,  leaving-  the 
reader  to  devise  similar  series  of  exercises 
for  other  forms. 


1, 

3. 

3. 

4. 

®                       0 

O          0          O 

ooooo 

ooooo 

o 

o                 o 

ooo 

o 

0                       0 

0                        0 

ooooooooo 

o 

0                       0 

ooo 

o 

0                      0 

0          O          O 

ooooo 

ooooo 

5, 

6. 

7. 

8. 

O    0    0    O    O 

006 

ooooo 

ooooo 

O                 O 

O        O        O 

o   o 

0    O           O    O 

O    O    O 

o   o       o  o 

ooooo 

O     O 

ooo 

0                 0 

O           0           O 

ooooooooo 

0                       0 

ooooo 

O     O 

000 

o            o 

O    O           0    O 

ooo 

o   o        o  o 

ooooo 

O                  O 

ooo 

0    0 

O    O    O    O    O 

ooo 

ooooo 

ooooo 

9. 

10. 

11. 

12. 

00           O     0 

0    O           O    0 

o  o       o  o 

0           0 

O                 O 

o            o 

o            o 

O    O     O    O     O 

ooooo 

o   o       o  o 

ooooo 

O 

o   o 

o   o 

ooooo 

ooo 

o 

ooo 

O 

0     0 

0     0 

ooooo 

ooooo 

O    0           O    O 

ooooo 

0                 O 

0                 O 

o            o 

O     0            O     O 

O    O           O    O 

o   o        o   o 

0          0 

13. 

14. 

15. 

16. 

O    O    O 

boo        ooooooooo 

.0 

O                0 

O                 O        O 

o 

o   o 

O    O          O    O 

ooooo    ° 

o 

ooo        ooo 

O    0 

0 

o 

0                           O 

O           O           O 

ooooo    o 

o 

0                         0 

0    O 

0 

0          O 

o 

O    O          O    O 

o  o  o  o  e    ° 

o     o- 

.  © 

0                 0 

O                G        ° 

0           O 

o 

O    O    0 

0    O    6            OOOOOOOOO 

O                         0 

0                          O 

ooo       ooo 

0    0 

o 

LENTILS    OR    DOTS. 


149 


ur.                  is. 

19.                       20. 

©-O©          OOO               O^"®^  ^O 

o 

o    ooo        ooo 

O        0    O       O          f£> 

OQ              O^o 

o>o     o    o_     o    o 

OOO         Jr 

o          o  o 

OO    o         O/-i     OQO     .-.Q 

°o       e°      / 

c°     e     °o   g 
o     o   o     o    Si 

0               0             o               ~Q              0" 

OQO             o        o 

0        ^°r,OO0^0           O°      o©n     °0 

o      QO°      °OXD      o    o    °o    o 

OOO           OOO       ^j 

0       0 

o 

~G    ooo        ooo 

0Q 

o 

OOOOQ 

o 

21. 

22. 

23. 

o°°0o 

0 

o 

ooooo 

0 

ooo        ooo 

o 

0           0           O 

o                  o 

o 

ooo 

ooooooooo 

ooooooooo 

o                        o 

o 

ooo 

0                                        0 

o 

ooo 

°00 

Q 

o 
ooooo 

0                          0 

ooo        ooo 

CL     _0 

°0° 

24. 

25. 

26. 

o 

ooooo 

0 

0     0 

o    o 

O    0 

OOOOO                       0 

0           0 

ooooo 

o                     oo 

o      oo 

0    0 

ooo            o 

ooooo   o 

ooo 

oo        o        oo         oo 

o      oo 

ooo      o      ooo 

o  ooooooooo   o       o 

0           O 

o  o   ooooo  o  o 

oo        o        oo 

o   o 

ooo      o      ooo 

ooo 

ooooo 

ooo 

o 

0     0 

ooooo 

ooooo 

0     0 

o   o 

o 

0 

27. 

28. 

29. 

o°°0o 

oon        ooo 
oo°o    ouoo 

ooooo 

0            O 

ooooo 

o 

o   o 

o   o   o   o 

oo        o        OQ 

o 

ooo 

o  o        o        o  o 

o   o 

o   o    o  o 

o    ooooooooo   o 

o        o 

ooooo 

ono         o         oo 
°o        o        o°             c 

o            o 
>                o 

8o°°   °°oo 

o 

ooooo 

o       o 

°o0o 

ISO 


PRIMARY    METHODS. 


80. 


o 
o 
o^oo 


o 

o     o 
ooo 


o   o 

o 
o   o 


,0 


,000 

°°oo 
o 


9P 


o0o 
o 


81. 


o  o 
o     o 

o 

o 

o 

o      o 
o  o 


o    o 

o 
o   o 


o  o 
o      o 
o 
o 
o 

o      o 
o  o 


o 

00 

o      o   o      o 
o  o      o  o 

,0°     O     O     °00 

o          go 

'00     O     O     ^0° 


o  o      o  o 
o      o    o      o 

OO 

o 


33.  34. 

ooo        ooo  ooooooooooo 
ooooo  o 

On    O     O     ^O    O     OOOOOOO     O 

Wrt       ^.^       ^U  Q  Q 

o    o 
ooooo 


o    o 
ooo 


o    o 

ooo    o    o 
o 


boo    ooc5   o    o 


o    o 


o   o 


35.  36. 

OOOOO     OOOOO    OOOn  Q 

o         o    o         o  o     cro    o^t 

OOOOOO    On     OOO 

o    o  o    o 
ooooooooooo 

o  o 
ooooooooooo 

O     O     O     O     O     O   O^     °n°n0 
O  00  O    O      0,0    O 

ooooo   ooooo  ^^ 


o     ooo     o 

o    o    o    o 

O    .-.OOOr,    O 
CkOX) 
^ 


o 

" 


ooo 


87. 


000 

o        o 

0                   0 

Oo°o0 
o 

0Oo0°0ooO°o0/ 

0 

0            00 

o 

o    o 

o 

o 

ooo         o 

o 

0     0 

0 

0 

o    o        o 

o 

0     0 

o 

0 

0 

ooo        o 
o        o   o 

nooooo    ooooo0 
ox                          Xo 

O                 0 

°00 

OOO     OO 

ooo~ 

0           0 

o 

0     0 

o 

ooo 

o 

o    o 

o 

0 

0     0 

0 

0 

nO°     °O 

£0°° 

0       OO   u 

o 

°°°£0 

39. 
o 

00. 

OQ          00' 
CQ00  O  O 

o  o 


o  o 


o  o        o 

00^0    O^ 


CO 

o 


o 
oo 


40. 

ooooooo 

o  o 

o  o  o  o 

o  o 

o        ooooo        o 

o        o 
o       o        o       o 

o        o 
o       ooooo       o 

o  o 

o  o  o  o 

o  o 

ooooooo 


o 
o 


41. 
o 

OO 

o  o 
.  o     o  / 

3O  O1 

o     o 

s    O    O 

'ocPA0 


o     o 

O    0O 


°0    0° 


o 
o 

0°0, 


o 

O 


LENTILS    OR    DOTS.  151 

42.  43.  44. 

O^OA     ^O^    •  00 

00    °0°    00  00 

o          o  oo          o  c>     _          o      o 

On  00  oO    OQOOO    O          O     OOOQp         O    O    O 

•6°o0       o     o       n°^>     cPoo      o     o       ooSb      oooo 

O     °00    O    O     00U    O  O   °00     O    O     00°    O          00     O     00 

o       °0f0q-.ou       o  o      °ocoq-,o°      o      oo      o     oo 

o         Rpo          °  o          xox          o      o  ooooo  o 

.0         0OT50U00         O  O         00°0d°00        O        00       o       CO 

o   Oo°  o  o   Uo0  o        o  no°  o  o  °o0  o       oo  o   oo 

0,0°        ,0       O         °OoO        Q0°         O       O         °0C0        OOOO 
O°  .G          O  ^O    ODOOO    O          O    OOOOO        O    O    O 

oo  oooo  oo 

°    O^o    °  OO^OOOn00  O    O 

0<b°°  °°c?0  <§v°°   D°c^ 

Fig.  1  indicates  the  square  with  the  help 
of  four  dots  placed  at  the  corners ;  its  out- 
lines are  formed  by  the  distances  between 
successive  dots ;  and  the  space  inclosed  in 
these  outlines.  Thus,  with  the  exception 
of  the  four  corners,  the  square  is  -wholly  a 
mental  creation.  In  Figs.  2  and  3  the  sides 
are  respectively  bisected  and  quadrisected. 
In  Figs.  4,  5,  and  6,  the  diameters  and 
diagonals  are  drawn.  Fig.  7  shows  the  four 
secondary  diagonals. 

Figs.  8-14  show  a  series  of  transformations 
of  the  square  introduced  by  Fig.  8.  For 
Fig.  9,  the  central  dot  of  each  side  of  the 
square  has  been  moved  inward,  near  the 
center  of  the  square. — For  Fig.  10,  the  cen- 
tral dot  of  each  side  has  been  placed  near 
one  of  the  corner  dots.  —  The  remaining 
transformations  will  explain  themselves. 


1B2  PRIMARY    METHODS. 

Figs.  15-21  show  a  series  of  transforma- 
tions of  the  outline  of  the  square  introduced 
by  Fig1.  15. — In  Fig.  16,  the  three  middle 
dots  of  each  side  were  moved  outward.— 
In  Fig.  17,  the  same  three  dots  were  moved 
inward.— In  Fig.  18,  the  sides  of  the  square 
curve  outward ;  in  Fig.  19,  they  curve  in- 
ward.—In  Figs.  20  and  21,  this  ^irvature 
is  limited  to  the  middle  five  dots  of  each 
side. 

Figs.  22-27  show  a  series  of  symmetrical 
patterns  "built  on  the  two  diameters  of  the 
square  (Fig.  22). 

Figs.  28-33  show  a  similar  series  of  pat- 
terns built  on  the  two  diagonals  of  the 
square  (Fig.  28). 

The  remaining  figures  -will  explain  them- 
selves sufficiently. 

Similar  series  of  exercises  may  be  con- 
trived on  the  basis  of  other  simple  geomet- 
rical figures — the  equilateral  triangle,  the 
circle,  the  lozenge,  the  hexagon,  etc. 

Again,  even  small  children  will  find  it  a 
comparatively  easy  task  to  "draw"  or  lay 
with  these  dots  the  outlines  of  all  kinds 
of  objects— houses,  trees,  pieces  of  furniture, 
tools,  flowers,  animals,  etc.  I  have-  seen 


LENTILS    OR    DOTS.  153 

quite  complicated  "picture  stories"  and 
landscapes  drawn  with  the  help  of  these  "by 
children,  five  to  seven  years  old. 


Lately  I  have  learned  to  use  the  dots  as 
a  most  convenient  help  in  experimental 
arithmetic.  A  few  specimen  solutions  will 
illustrate  this,  and  suggest  an  abundance 
of  useful  exercises  and  ways. 

The  following  examples  were  given  by 
pupils  in  a  class  exercise  with  children  of 
the  third  grade,  and  solved  experimentally 
"by  the  class  with  the  help  of  dots.  Each 
child  had  received  fifty  dots. 

(1)  John  had  25  cents.  He  lost  3  cents, 
and  spent  15  cents  for  a  "book.  How  many 
cents  had  he  left  ? 

SOLUTION. — The  children  first  laid  down  25 
dots,  to  represent  the  25  cents,  taking  care 

to  lay  them  "by   tens,    thus:      oooooooooo; 

oooooooooo 
they  then  removed  three  dots      o  o  o  o  o 

for  three  cents  lost,  and,  lastly,  fifteen  dots 
for  the  15  cents  spent,  leaving  the  re- 
mainder thus:  ooooooo. 

A  few  children  had  placed  their  dots  on 
their  slates,  and  then,  -without  removing 


154  PRIMARY     METHODS. 

any  of  them,  counted  off  the  required  num- 
bers   and   made    marks   with.       0000000)000 

oooooooooo 
their  pencils.     Thus,  in  this      oo|ooo 

example,    three    are    counted    off,    and   then 
fifteen,  a  vertical  mark  indicating1  the  steps. 

(2)  Harry    received     12     cents     from    his 
father,   9   cents  from  his  mother,    his    sister 
gave    him   4    cents,   and   he   found   2    cents. 
How  many  cents  had  he  in  all  ? 

SOLUTIONS:   a.  b-  c  (on  slates), 

oooooooooo    oooooooooo    oooooooooo 
oo  oooooooooo    oo|oooooooo 

OOOOOOOOO          OOO.OOOO  O|OOOO|OO 

o  ooo 

00 

(3)  How  many  pencils    at    4  cents    apiece 
can  Harry  "buy  with  his  money? 

SOLUTIONS  :   a.  o  o  o  o  o  0  b  (on  slates).o  o  o  olo  o  o  olo  o 

OOO  OOO  OO|OO  O  O|OOOQ] 

oooooo     ooo  oooo|ooo 

o  ooooo 

(4)  My  father  gave  us  36    pennies.     How 
many    did    each    one    of  us    (four    children) 
get? 

SOLUTIONS :  a.ooooooooo     b  (on slates)p OQOOOOOQ 

OOOOOOOOO  OOOOOOOOO 

OOOOOOOOO  OOOOOOOOO 

OOOOOOOOO  OOOOOOOOO 

(5)  What  will  2£  pounds  of  coffee  cost,  at 
18  cents  per  pound? 


LENTILS    OR    DOTS.  155 

SOLUTIONS :  a.  oooooooooo        oooooooO 

OOOOOOOOOO    OOOOOOOO 

ooooooooo 

b.  c., 

OOOOOOOOOO  OOOOOOOOO 

OOOOOOOOOO  OOOOOOOOO 

OOOOOOOOOO  OOOOOOOOO 

OOOOOOOOOO  OOOOOOOOO 

OOOOO  OOOOOOOOO 

(6)  A  grocer   mixed    one   pound   of   sugar 
worth   7  cents,  one   pound    of   sugar    worth 
8  cents,   and  one  pound  of  sugar  worth    12 
cents.      How    much    is    one    pound     of    the 
mixture  worth  ?     (This   problem  was   given 
"by  the  teacher.) 

SOLUTIONS;  a.  b. 

OOOOOOOOO  OOOOO  OO|O  O 

DOOOOOOOO  O  OOP  O  O  O  O|O 

OOOOOOOOO  OOOOOOOOO 

[In  (a)  the  child  counted  from  top  to 
bottom  beginning  on  the  left,  successively 
7,  8,  12 ;  in  (5)  he  laid  in  the  first  hori- 
zontal row  7,  in  the  second  8,  in  the  third 
8 ;  then  filled  up  the  rows  with  the  re- 
maining 4.] 

(7)  How  many  dozen  in  50  eggs  ? 

SOLUTIONS:  a.  b. 

OOOOOOOOOO   OO     OOOOOOOOOO 

OOOOOOOOOO   OO    O  O 

OOOOOOOOOO   OO     OOOOOOOOOO 

OOOOOOOOOO   OO     OO OO 

OO    OOOOOOOOOO 

00 

OOOOOOOOOO 
00 


156 


PRIMARY    METHODS. 


(8)    How  many  quarts  of  milk  in  8£   gal- 
lons ? 


SOLUTIONS :  a. 

0000      OOOO 
'OOOO      OOOO 


OOOO 

OOOO 

OOOO 

OOOO 

oo 

b. 

OOOO 

OOOO 

OOOO 

OOOO 

OOOO 

OOOO 

OOOO 

00 

OOOO 


(9)  A  man  sold  5  cows,  and  gained  45 
dollars.  How  much  did  he  make  on  each 
cow  ? 


SOLUTION :  ooooooooo 
ooooooooo 
ooooooooo 
ooooooooo 
ooooooooo 


CHAPTER    XIX. 

THE  GROUP  TABLE. 

tHE  group  table  is  a  modified  kindergar- 
ten table,  adapted  to  the  requirements 
of  social  work  with  the  material  described 
in  this  volume,  as  well  as  -with  other  occu- 
pation material.  The  table  I  now  use  at 
La  Porte  is  thirty  inches  square  and  twenty- 
two  inches  high.  The  top  is  ruled  in  square 
inches,  like  the  ordinary  kindergarten  table. 
The  center  is  marked  in  some  convenient 
way.  When  it  is  in  use,  four  children  are 
seated  around  it  on  low  chairs  or  stools ; 
each  child  sitting  in  front  of  the  middle 
of  one  of  the  sides.  In  the  exercises,  each 
child  represents  the  side  before  it  or  the 
corner  on  the  right  or  left,  so  that  with  its 
help  a  kind  of  rhythmic  life  is  imparted 
to  the  square. 

A  few  typical  exercises  will  best  illus- 
trate its  use. 

In  Fig.   1,  the  outline  of  the  large  square 


138  PRIMARY    METHODS. 

represents  the  edges  of  the  group  ta"ble. 
The  children  are  seated  in  front  of  the 
points  a,  6,  c,  and  d.  The  center  of  the  table 
is  marked  with  a  cross  (X).  Each  child  has 
received  for  work  twelve  cubical  blocks 
which  he  has  placed  (by  direction)  in  a  row 
from  right  to  left  two  inches  behind  the 
edge  of  the  table.  For  my  convenience  in 
the  description  of  the  following  exercises,  I 
have  marked  the  cubes  in  the  diagram  with 
the  figures  1-6  from  both  ends  of  the  row. 
The  diagram  presents  two  exercises :  the 
first  near  the  margin,  the  second  around 
the  center  of  the  diagram.  For  the  first 
exercise  the  two  central  blocks  (6,  6)  of  the 
original  row  remain  stationary.  The  re- 
mainder are  moved  by  the  children  in  ac- 
cordance with  the  following  dictation,  by 
the  teacher  or  by  an  older  pupil:  "With  the 
right  hand  move  the  five  cubes  on  the 
right  back  one  inch ; — with  the  left  hand 
the  five  cubes  on  the  left  back  one  inch.— 
With  the  left  hand  move  the  four  cubes  on 
the  left  back  one  inch ; — with  the  right 
hand  the  four  on  the  right  back  one  inch. 
-With  the  right  hand  move  the  three 
cubes  on  the  right  back  one  inch ; — with 


THE     GROUP     TABLE.  159 

the  left  hand  tile  three  cubes  on  the  left 
back  one  inch. — With  both  hands  move  the 
two  cubes  on  the  left  and  the  two  on  the 
right  back  one  inch. — With  both  hands 
move  one  cube  on  the  left  and  one  on  the 
right  back  one  inch."  At  each  symmetric 
phase — indicated  in  the  dictation  by  a  period 
and  dash — the  teacher  should  pause  to  give 
the  children  an  opportunity  for  observing 
the  social  or  group  value  of  the  form  ob- 
tained. 

For  the  second  exercise — indicated  in  the 
central  form — the  following  dictation  is  in 
place:  ''With  both  hands  move  the  outside 
blocks  (1)  inward  (each)  five  inches, — back 
six  inches.— With  both  hands  move  the  next 
outside  blocks  (2)  inward  three  inches, — 
backward  six  inches.  —  With  both  hands 
move  the  next  outside  cubes  (3)  inward  one 
inch, — backward  six  inches.  —  With  both 
hands  move  the  next  outside  cubes  (4)  in- 
ward one  inch, — backward  six  inches. — With 
both  hands  move  the  next  outside  cubes 
(5)  backward  six  inches, — inward  one  inch. 
With  both  hands  move  the  last  blocks 
backward  six  inches." 

Here  again  it  is  desirable  that  the  teacher 


160 


PRIMARY    METHODS. 


should  pause  at  eacli  symmetric  phase  to 
give  tlie  children  an  opportunity  to  observe 
their  work.  The  influence  of  this  "work  on 
the  social  instincts  of  the  children  is  ob- 

FlG.  1. 


-Cr1 


m  -e- 


vious.  However  much  each  one  may  at  the 
beginning  be  interested  in  his  own  cubes, 
this  individual  ownership  is  soon  lost  sight 
of  in  the  joy  of  the  common  'work,  in  the 


THE     GROUP     TABLE. 


161 


results  of  "owr"  work.  I  have  never  yet 
found  a  child  that  had  the  hardihood  to 
claim  his  share  of  the  material  as  his  own, 
after  completion  of  the  group  form. 

FIG.  2. 


P 


In  Fig.  2,  I  have  represented  the  result 
of  the  joint  invention  of  a  group  of  four 
children  in  the  second  grade  of  a  primary 
school.  Each  child  had  received  twenty 


162 


PRIMARY     METHODS. 


cubes  ("four  fives,"  as  the  teacher  said). 
The  teacher  had  indicated  the  center  of  the 
table  by  placing1  a  cube  in  the  spot  indi- 
cated by  a  cross  ( x )  in  our  figure,  and  then 

Fia.  3. 


fl|fl|g|fi|fl|o| 


-a 


E 

i 
7 

1 

1 

f\ 

g 

/ 

1 

A 

0 

/ 

i 

Cr. 

ft 

i 

1 

?-. 

0      . 

I        0 

ZTZ: 

,  ^ 

^ 

•^     , 



- 

1~ 

SJC 

~ 

• 

r 

£ 

2 

£ 

0       ' 

r     0 

•-i 

1 

» 

]/ 

« 

1 

/ 

g 

~ 

( 

/ 

b 

Is. 

1 

1 

) 
1 

±J 

b- 


|r|o|l/[6r|b|-»|D|fc|(/|l/[o|r| 

d 


left  the  children  to  the  rule  of  their  "game" 
of  Follow  the  leader.  This  rule  is  simple.  One 
of  the  children  (a)  begins,  places  a  block 
(in  this  case  [1]).  He  is  followed  in  the 


THE     GROUP    TABLE. 


163 


same  movement  by  the  child  on  the  oppo- 
site side  (&),  and  this  one  is  followed  "by 
the  remaining1  children  (c  and  d),  who  place 
the  corresponding  blocks  simultaneously. 
The  next  move  (2)  is  originated  by  the 


F 

EG. 

a 

4. 

j, 

j, 

a 

X 

o 

» 

0 

.1 

J, 

II 

ft 

ft 

j 

J, 

r, 

0 

/) 

J 

-. 

* 

-* 

.( 

<i 

q 

'/ 

%- 

k     W     (• 

~. 

O 

•-c 

<Q 

iy 

a 

a 

c> 

A 

Cs     ?5      O       i» 

c^ 

1 

0 

5= 

«a 

9 

e 

? 

r3 

CB    5s    o    i.    ? 

s 

o 

•-- 

<Q 

& 

e 

V 

V 

^5 

CS     ?»     0      S- 

-* 

-5 

•* 

-5 

b 

b 

b 

r 

!.%.(• 

r 

0 

0 

0 

r 

r 

y 

11 

V 

r 

r 

0 

0 

o 

r 

r 

r 

r 

V 

child  (6),  the  third  move  (3)  by  the  child 
(c),  the  next  (4)  by  the  child  (d).  Then  it 
is  again  (a)'s  turn,  and  the  game  continues 
until  the  material  is  exhausted. 

Here  both  the  conception  and  the  work 
are  common,  belong  not  to  any  individual 
child,  but  to  the  group  as  a  'whole.  The 
pattern  is  a  common  finding  or  invention, 


164 


PRIMARY    METHODS. 


drawing-  in  its  growth,  equally  on  the  pow- 
ers of  all  the  children. 

Figs.  3  and  4  are  illustrations  of  color 
exercises  with  the  aid  of  colored  cubes. 
Fig.  3  is  a  dictation  exercise  in  the  rainbow 


FIG.  5. 


colors.  The  pupils  have  received  twelve 
blocks,  two  of  each  of  the  six  colors.  By 
dictation,  these  are  placed  in  a  certain  order 
—here  indicated  by  the  initial  letters  of  the 
color  names— from  left  to  right,  ready  for 


THE     GROUP    TABLE. 


163 


use.  The  central  figure  results  from,  suit- 
able dictation  for  moving  the  cubes  inward. 
Fig-.  4  is  an  invention  of  the  group  of 
children. 

Figs.   5   and  6  present  similar  suggestions 


Fia.  6 


with  sticks  or  splints.  In  Fig.  5  two-inch 
sticks — plain  or  colored — are  used  for  a  dic- 
tation. Fig.  6  reports  the  invention  of  a 
group  of  children  with  the  help  of  one-inch 
and  two-inch  sticks- 


166  PRIMARY     METHODS. 

These  suggestions  must  suffice.  The  gain 
from  these  exercises  in  the  development  of 
social  virtue  constitute  their  chief  value. 
The  fact  that  the  union  of  the  group  in 
aim  and  effort  is  essential  to  success  is  so 
prominent  that  a  distinct  group  conscious- 
ness is  horn  which  makes  the  four  pecul- 
iarly and  distinctly  one.  On  the  other 
hand,  the  importance  of  each  member  of 
the  group  as  an  indispensable  part  thereof 
is  so  obvious,  that  both  self-esteem  and 
social  esteem  grow  apace  but  in  healthy 
union,  one  aiding  the  other.  Thus  the 
child  is  protected  equally  against  the  one- 
sided excrescences  of  self-conceit  and  self- 
abasement,  and  gains  equally  in  individual 
and  social  vigor.  The  child  is  distinctly 
conscious  that  by  this  co-ordination  and 
inordination  in  a  union  with  equals,  self  is 
lifted  into  a  higher  order  of  being,  and 
eagerly  gives  all  he  has  and  is  to  the  pur- 
poses of  the  little  group. 


THE  NATIONAL   SERIES  OF  STANDARD  SCHOOL-BOOKS. 


GENERAL    HISTORY. 

Monteith's  Youth's  History  of  the  United  States. 

A  History  of  the  United  States  for  beginners.  It  is  arranged  upon  the  catechetical  plan, 
with  illustrative  maps  and  engravings,  review  questions,  dates  in  parentheses  (that  their 
study  may  be  optional  with  the  younger  class  of  learners),  and  interesting  biographical 
sketches  of  all  persons  who  have  been  prominently  identified  with  the  history  of  our 

country. 

Willard's  United  States.     School  and  University  Editions. 

The  plan  of  this  standard  work  is  chronologically  exhibited  in  front  of  the  titlepage. 
The  maps  and  sketches  are  found  useful  assistants  to  the  memory  ;  and  dates,  usually 
so  difficult  to  remember,  are  so  systematically  arranged  as  in  a  great  degree  to  obviate 
the  difficulty.  Candor,  impartiality,  and  accuracy  are  the  distinguishing  features  of 
the  narrative,  portion. 

Willard's  Universal  History.     New  Edition. 

The  most  valuable  features  of  the  "  United  States  "  are  reproduced  in  this.  The 
peculiarities  of  the  work  are  its  great  conciseness  and  the  prominence  given  to  the 
chronological  order  of  events.  The  margin  marks  each  successive  era  with  great  dis* 
tinctness,  so  that  the  pupil  retains  not  only  the  event  but  its  time,  and  thus  fixes  the 
order  of  history  firmly  and  usefully  in  his  mind.  Mrs.  Willard's  books  are  constantly 
revised,  and  at  all  times  written  up  to  embrace  important  historical  events  of  recent 
date.  Professor  Arthur  Oilman  has  edited  the  last  twenty-five  years  to  1882. 

Lancaster's  English  History. 

'  By  the  Master  of  the  Stoughton  Grammar  School,  Boston.  The  most  practical  of  the 
"  brief  books."  Though  short,  it  is  not  a  bare  and  uninteresting  outline,  but  contains 
enough  of  explanation  and  detai  1  to  make  intelligible  the  cause  and  rffrct  of  events. 
Their  relations  to  the  history  and  development  of  the  American  people  is  made  specially 
prominent. 

Willis's  Historical  Reader. 

Being  Collier's  Great  Events  of  History  adapted  to  American  schools.  This  rare 
epitome  of  general  history,  remarkable  for  its  charming  style  and  judicious  selection  of 
events  on  which  the  destinies  of  nations  have  turned,  has  been  skilfully  manipulated 
by  Professor  Willis,  with  as  few  changes  as  would  bring  the  United  States  into  its  proper 
position  in  the  historical  perspective.  As  reader  or  text-book  it  has  few  equals  and  no 
superior. 

Berard's  History  of  England. 

By  an  authoress  well  known  for  the  success  of  her  History  of  the  United  States, 
The  social  life  of  the  English  people  is  felicitously  interwoven,  as  in  fact,  with  the  civil 
and  military  transactions  of  the  realm. 

Ricord's  History  of  Rome. 

Possesses  the  charm  of  an  attractive  romance.  The  fables  with  which  this  history 
abounds  are  introduced  in  such  a  way  as  not  to  d«>ceive  the  inexperienced,  while  adding 
materially  to  the  value  of  the  work  as  a  reliable  index  to  the  character  and  institutions, 
as  well  as  the  historv  of  the  Roman  people. 

35 


THE  NATIONAL   SERIES  OF  STANDARD   SCHOOL-BOOKS. 

HISTORY  —  Continued. 

Hanna's  Bible  History. 

The  only  compendium  of  Bible  narrative  which  affords  a  connected  and  chronological 
view  of  the  important  events  there  recorded,  divested  of  all  superfluous  detail 

Summary  of  History;  American,  French,  and  English. 

A  well-proportioned  outline  of  leading  events,  condensing  the  substance  of  the  more 
extensive  text-books  in  common  use  into  a  series  of  statements  so  brief,  that  every 
word  may  be  committed  to  memory,  and  yet  so  comprehensive  that  it  presents  an 
accurate  though  general  view  of  the  whole  continuous  life  of  nations. 

Marsh's  Ecclesiastical  History. 

Affording  the  History  of  the  Church  in  all  ages,  with  accounts  of  the  pagan  world 
during  the  biblical  periods,  and  the  character,  rise,  and  progress  of  all  religions,  as  well 
as  the  various  sects  of  the  worshippers  of  Christ.  The  work  is  entirely  non-sectarian, 
though  strictly  catholic.  A  separate  volume  contains  carefully  prepared  questions  for 
class  use. 

Mill's  History  of  the  Ancient  Hebrews. 

With  valuable  Chronological  Charts,  prepared  by  Professor  Edwards  of  N.  Y.  This 
is  a  succinct  account  of  the  chosen  people  of  God  to  the  time  of  the  destruction  of 
Jerusalem.  Complete  in  one  volume. 

Topical  History  Chart  Book. 

By  Miss  Ida  P.  Whitcomb.  To  be  used  in  connection  with  any  History,  Ancient  or 
Modern,  instead  of  the  ordinary  blank  book  for  summary.  It  embodies  the  names  of 
contemporary  rulers  from  the  earliest  to  the  present  time,  with  blanks  under  each,  in 
which  the  pupil  may  write  the  summary  of  the  life  of  the  ruler. 

Oilman's  First  Steps  in  General  History. 

A  "suggestive  outline"  of  rare  compactness.  Each  country  is  treated  by  itself,  and 
the  United  States  receive  special  attention.  Frequent  maps,  contemporary  events  in 
tables,  references  to  standard  works  for  fuller  details,  and  a  minute  Index  constitute 
the  "  Illustrative  Apparatus."  From  no  other  work  that  we  know  of  can  so  succinct  a 
view  of  the  world's  history  be  obtained.  Considering  the  necessary  limitation  of  space, 
the  style  is  surprisingly  vivid,  and  at  times  even  ornate.  In  all  respects  a  charming, 
though  not  the  less  practical,  text-book. 

Baker's  Brief  History  of  Texas. 
Dimitry's  History  of  Louisana. 
Alison's  Napoleon  First. 

The  history  of  Europe  from  1788  to  1815.  By  Archibald  Alison.  Abridged  by  Edward 
S.  Gould.  One  vol.,  8vo,  with  appendix,  questions,  and  maps.  550  pages. 

Lord's  Points  of. History. 

The  salient  points  in  the  history  of  the  world  arranged  catechetically  for  class  use  or 
for  review  and  examination  of  teacher  or  pupil.  By  John  Lord,  LL.D.  12mo,  300 
pages. 

Carrington's  Battle  Maps  and  Charts  of  the  American 
Revolution. 

Topographical  Maps  and  Chronological  Charts  of  every  battle,  with  3  steel  portrait* 
of  Washington.  8vo,  cloth. 

Condit's  History  of  the  English  Bible. 

For  theological  and  historical  students  this  book  has  an  intrinsic  value.  It  gives  the 
history  of  all  the  English  translations  down  to  the  present  time,  together  with  a  careful 
review  of  their  influence  upon  English  literature  and  language. 

36 


THE  NATIONAL   SERIES   OF  STANDARD  SCHOOL-BOOKS. 


DRAWING. 

BARNES'S     POPULAR     DRAWING     SERIES. 

Based  upon  the  experience  of  the  most  successful  teachers  of  drawing  in  the  United 
States. 

The  Primary  Course,  consisting  of  a  manual,  ten  cards,  and  three  primary 
AtMTing  hooks,  A,  B,  and  C. 

Intermediate  Course.    Four  numbers  aiid  a  manual. 

Advanced  Course.    Four  numbers  and  a  manual 

Instrumental  Course.    Four  numbers  and  a  manual. 

The  Intermediate,  Advanced,  and  Instrumental  Courses  are  furnished  either  in  book 
or  card  form  at  the  same  prices.  The  books  contain  the  usual  blanks,  with  the  unusual 
advantage  of  opening  from  the  pupil,  —  placing  the  copy  directly  in  front  and  above 
the  blank,  thus  occupying  but  little  desk-room.  The  cards  are  in  the  end  more  econom- 
ical than  the  books,  if  used  in  connection  with  the  patent  blank  folios  that  accompany 
this  series. 

The  card*  are  arranged  to  be  bound  (or  tied)  in  the  folios  and  removed  at  pleasure. 
The  pupil  at  the  end  of  each  number  has  a  complete  book,  containing  only  his  own 
work,  while  the  copies  are  preserved  and  inserted  in  another  folio  ready  for  use  in  the 
next  class. 

Patent  Blank  Folios.  No.  1.  Adapted  to  Intermediate  Course.  No.  2.  Adapted 
to  Advanced  and  Instrumental  Courses. 

ADVANTAGES  OF  THIS  SERIES. 

The  Plan  and  Arrangement.  —  The  examples  are  so  arranged  that  teachers  and 
pupils  can  see,  at  a  glance,  how  they  are  to  be  treated  and  where  they  are  to  be  copied. 
In  this  system,  copying  and  designing  do  not  receive  all  the  attention.  The  plan  is 
broader  in  its  aims,  dealing  with  drawing  as  a  branch  of  common-school  instruction, 
and  giving  it  a  wide  educational  value. 

Correct  Methods.  —  In  this  system  the  pupil  is  led  to  rely  upon  himself,  and  not 
upon  delusive  mechanical  aids,  as  printed  guide-marks,  &c. 

One  of  the  principal  objects  of  any  good  course  in  freehand  drawing  is  to  educate  the 
eye  to  estimate  location,  form,  and  size.  A  system  which  weakens  the  motive  or  re- 
moves the  necessity  of  thinking  is  false  in  theory  and  ruinous  in  practice.  The  object 
should  be  to  educate,  not  cram  ;  to  develop  the  intelligence,  not  teach  tricks. 

Artistic  Effect.— The  beauty  of  the  examples  is  not  destroyed  by  crowding  the 
pages  with  useless  and  badly  printed  text  The  Manuals  contain  all  necessary 
instruction. 

Stages  of  Development. —Many  of  the  examples  are  accompanied  by  diagrams, 
showing  the  dilt'erent  stages  of  development. 

Lithographed  Examples. —  The  examples  are  printed  in  imitation  of  pencil 
drawing  (not  in  hard,  black  lines)  that  the  pupil's  work  may  resemble  them. 

One  Term's  Work.  —  Each  book  contains  what  can  be  accomplished  in  an  average 
term,  and  no  more.  Thus  a  pupil  finishes  one  book  before  beginning  another. 

Quality  —  not  Quantity.  —  Success  in  drawing  depends  upon  the  amount  of  thought 
exercised  by  the  pupil,  and  not  upon  the  large  njimber  of  examples  drawn. 

Designing.  —  Elementary  design  is  more  skilfully  taught  in  this  system  than  by 
any  other.  In  addition  to  the  instruction  given  in  the  books,  the  pupil  will  find  printed 
on  the  insides  of  the  covers  a  variety  of  beautiful  patterns. 

Enlargement  and  Reduction.  — The  practice  of  enlarging  and  reducing  from 
copies  is  not  commenced  until  the  pupil  is  well  advanced  in  the  course  and  therefore 
better  able  to  cope  with  this  difficult  feature  in  drawing. 

Natural  Forms.  —This  is  the  only  course  that  gives  at  convenient  intervals  easy 
and  progressive  exercises  in  the  drawing  of  natural  forms. 

Economy.  —  By  the  patent  binding  described  above,  the  copies  need  not  be  thrown 
aside  when  a  book  is  filled  out,  but  are  preserved  in  perfect  condition  for  future  use. 
The  blank  books,  only,  will  have  to  be  purchased  after  the  first  introduction,  thus  effect- 
ing a  saving  of  more  than  half  in  the  usual  cost  of  drawing-books. 

Manuals  for  Teachers.  — The  Manuals  accompanying  this  series  contain  practical 
instructions  for  conducting  drawing  in  the  class-room,  with  definite  directions  for  draw- 
ing each  of  the  examples  in  the  books,  instructions  for  designing,  model  and  object 
drawing,  drawing  from  natural  forms,  &c. 

38 


THE  NATIONAL   SERIES  OF  STANDARD  SCHOOL-BOOKS. 

FAMILIAR    SCIENCE. 

Norton  &  Porter's  First  Book  of  Science. 

Sets  firth  the  principles  of  Natural  Philosophy,  Astronomy,  Chemistry,  Physiology, 
and  Geology,  on  the  catechetical  plan  for  primary  classes  an  I  beginners. 

Chambers's  Treasury  of  Knowledge. 

Progressive  lessons  upon  — first,  common  things  which  lie  most  immediately  around 
us,  and  first  attract  the  attention  of  the  young  mind ;  second,  common  objects  from  the, 
(mineral,  animal,  and  vegetable  kingdoms,  manufactured  articles,  and  miscellaneous 
substances  ;  third,  a  systematic  view  of  nature  under  the  various  sciences.  May  be 
used  as  a  reader  or  text-book. 

Monteith's  Easy  Lessons  in  Popular  Science. 

This  book  combines  within  its  covers  more  attractive  features  for  the  study  of  science 
by  children  than  any  other  book  published.  It  is  a  reading  book,  spelling  book,  com- 
position book,  drawing  book,  geography,  history,  book  on  botany,  zoology,  agricul- 
ture, manufactures,  commerce,  and  natural  philosophy.  All  these  subjects  are  presented 
in  a  simple  and  effective  style,  such  as  would  be  adopted  by  a  good  teacher  on  an 
excursion  with  a  class.  The  class  are  supposed  to  be  taking  excursions,  \7ith  the  help 
of  a  large  pictorial  chart  of  geography,  which  can  be  suspended  before  them  in  the 
school-room.  A  key  of  the  chart  is  inserted  in  every  copy  of  the  book.  With  tlm 
book  the  science  of  common  or  familiar  things  car;  be  taught  to  beginners. 


NATURAL    PHILOSOPHY. 

Norton's  First  Book  in  Natural  Philosophy. 
Peck's  Elements  of  Mechanics. 

A  suitable  introduction  to  Bartlett's  higher  treatises  on  Mechanical  Philosophy,  and 
adequate  in  itself  for  a  complete  academical  course. 

Bartlett's  Analytical  Mechanics. 
Bartlett's  Acoustics  and  Optics. 

A  complete  system  of  Collegiate  Philosophy,  by  Prof.  W.  H.  C.  Bartlett,  of  West 
Point  Military  Academy. 

Steele's  Physics. 

Peck's  Ganot.  

GEOLOGY. 

Page's  Elements  of  Geology. 

A  volume  of  Chambers's  Educational  Course.  Practical,  simple,  and  eminently 
calculated  to  make  the  study  interesting. 

Steele's  Geology. 

CHEMISTRY. 

Porter's  First  Book  of  Chemistry. 
Porter's  Principles  of  Chemistry. 

The  above  are  widely  known  as  the  productions  of  one  of  the  most  eminent  scientific 
men  of  America.  The  extreme  simplicity  in  the  method  of  presenting  the  science,  while 
exhaustively  treated,  has  excited  universal  commendation. 

Gregory's  Chemistry  (Organic  and  Inorganic).     2  vols. 

The  science  exhaustively  treated.     For  colleges  and  medical  students. 

Steele's  Chemistry. 

47 


THE  NATIONAL   SERIES   OF  STANDARD  SCHOOL-BOOKS. 

NATURAL   SCIENCE  —  Continued. 

ASTRONOMY. 

Peck's  Popular  Astronomy. 

By  Win.  G.  Peck,  Ph.D.,  LL.D.,  Professor  of  Mathematics,  Mechanics,  and  Astron- 
omy in  Columbia  College.  12mo.  Cloth.  330  pages. 

Professor  Peck  has  here  produced  a  scientific  work  in  brief  form  for  colleges,  acade- 
mies, and  high  schools.  Teachers  who  do  not  want  an  elementary  work  —  like  Steele's 
.  Astronomy,  for  instance  —  will  find  what  they  want  in  this  book.  Its  discussion  of  the 
Stars,  Solar  System,  Earth,  Moon,  Sun  and  Planets,  Eclipses,  Tides,  Calendars,  Planets 
and  Satellites.  Comets  and  Meteors,  &c.,  is  full  and  satisfactory.  The  illustrations  are 
numerous  and  very  carefully  engraved,  so  the  student  can  gain  an  accurate  comprehen- 
sion of  the  things  represented.  Professor  Peck  is  wonderfully  clear  and  concise  in  his 
style  of  writing,  and  there  is  nothing  redundant  or  obscure  in  this  work.  It  is  intended 
for  popular  as  well  as  class  nse,  and  accordingly  avoids  too  great  attention  to  mathe- 
matical processes,  which  are  introduced  in  smaller  type  than  the  regular  text.  For 
higher  schools  this  astronomy  is  undoubtedly  the  best  text-book  yet  published. 

Willard's  School  Astronomy. 

By  means  of  clear  and  attractive  illustrations,  addressing  the  eye  in  many  cases  by 
analogies,  careful  definitions  of  all  necessary  technical  terms,  a  careful  avoidance  of 
verbiage  and  unimportant  matter,  particular  attention  to  analysis,  and  a  general  adop- 
tion of  the  simplest  methods,  Mrs.  Willard  has  made  the  best  and  most  attractive 
elementary  Astronomy  extant. 

Mclntyre's  Astronomy  and  the  Globes. 

A  complete  treatise  for  intermediate  classes.     Highly  approved. 

Bartlett's  Spherical  Astronomy. 

The  West  Point  Course,  for  advanced  classes,  with  applications  to  the  current  wants 
of  Navigation,  Geography,  and  Chronology. 


NATURAL    HISTORY. 

Carll's  Child's  Book  of  Natural  History. 

Illustrating  the  animal,  vegetable,  and  mineral  kingdoms,  with  application  to  the 
arts.     For  beginners.     Beautifully  and  copiously  illustrated. 

Anatomical  Technology.     Wilder  &  Gage. 

As  applied  to  the  domestic  cat.    For  the  use  of  students  of  medicine. 


ZOOLOGY. 

Chambers's  Elements  of  Zoology. 

A  complete  and  comprehensive  system  of  Zoology,  adapted  for  academic  instruction, 
presenting  a  systematic  view  of  the  animal  kingdom  as  a  portion  of  external  nature. 


ROADS    AND    RAILROADS. 

Gillespie's  Roads  and  Railroads. 

Tenth  Edition.     Edited  by  Cady  Staley,  A.M.,  C.E.     464  pages.     12mo.    Cloth. 

This  book  has  long  been  and  still  is  the  standard  manual  of  the  principles  and  prac- 
tice of  Road-making,  comprising  the  location,  construction,  and  Improvement  of  roads 
ii-cimmiin,  macadam,  paved,  plank,  &c.)  and  railroads.  It  was  compiled  by  Win. 
Gillespie,  LL.D.,  C.E.,  of  Union  College. 

49 


THE  NATIONAL   SERIES   OF  STANDARD   SCHOOL-BOOKS. 


AESTHETICS. 

Huntington's  Manual  of  the  Fine  Arts., 

A  view  of  the  rise  and  progress  of  art  in  different  countries,  a  brief  account  of  the 
most  eminent  masters  of  art,  and  an  analysis  of  the  principles  ot  art.  It  is  complete 
in  itself,  or  may  precede  to  advantage  the  critical  work  of  Lord  Kames. 

Boyd's  Kames's  Elements  of  Criticism. 

The  best  edition  of  this  standard  work ;  without  the  study  of  which  none  may  be 
considered  proficient  in  the  science  of  the  perceptions.  No  other  study  can  be  pursued 
with  so  marked  an  effect  upon  the  taste  and  refinement  of  the  pupil 


ELOCUTION. 

Watson's  Practical  Elocution. 

A  scientific  presentment  of  accepted  principles  of  elocutionary  drill,  with  black- 
board diagrams  and  full  collection  of  examples  for  class  drill  Cloth.  90  pages,  liimo. 

Taverner  Graham's   Reasonable  Elocution. 

Based  upon  the  belief  that  true  elocution  is  the  right  interpretation  of  thought, 
and  guiding  the  student  to  an  intelligent  appreciation,  instead  of  a  merely  mechanical 
knowledge,  of  its  rules. 

Zachos's  Analytic  Elocution. 

All  departments  of  elocution  —  such  as  the  analysis  of  the  voice  and  the  sentence, 
phonology,  rhythm,  expression,  gesture,  &c.  —  are  here  arranged  for  instruction  in 
classes,  illustrated  by  copious  examples. 


SPEAKERS. 

Northend's  Little  Orator. 
Northend's  Child's  Speaker. 

Two  little  works  of  the  same  grade  but  different  selections,  containing  simple  and 
attractive  pieces  for  children  under  twelve  years  of  age. 

Northend's  Young  Declaimer. 
Northend's  National  Orator. 

Two  volumes  of  prose,  poetry,  and  dialogue,  adapted  to  intermediate  and  grammar 
classes  respectively. 

Northend's  Entertaining  Dialogues. 

Extracts  eminently  adapted  to  cultivate  the  dramatic  faculties,  at  well  as  entertain. 

Oakey's  Dialogues  and  Conversations. 

For  school  exercises  and  exhibitions,  combining  useful  instruction. 

James's  Southern  Selections,  for  Reading  and  Oratory 

Embracing  exclusively  Southern  literature. 

Swett's  Common  School  Speaker. 
Raymond's  Patriotic  Speaker. 

A  superb  compilation  of  modern  eloquence    and  poetry,  with   original  dramatic 
exerci»«s.    Ksariy  every  eminent  modern  orator  is  represented. 

52 


THE  NATIONAL   SERIES  OF  STANDARD  SCHOOL-BOOKS. 


MIND. 
Mohan's  Intellectual  Philosophy. 

The  subject  exhaustively  considered.  The  author  has  evinced  learning,  candor,  and 
independent  thinking. 

Mahan's  Science  of  Logic. 

A  profound  analysis  of  the  laws  of  thought.  The  system  possesses  the  merit  of  being 
intelligible  and  self-consistent.  In  addition  to  the  author's  carefully  elaborated  views, 
it  embraces  results  attained  by  the  ablest  minds  of  Great  Britain,  Germany,  and  France, 
in  this  department 

Boyd's  Elements  of  Logic. 

A  systematic  and  philosophic  condensation  of  the  subject,  fortified  with  additions 
from  Watts,  Abercrombie,  Whately,  &c. 

Watts  on  the  Mind.     Edited  by  Stephen  N.  Fellows. 

The  "  Improvement  of  the  Mind,"  by  Isaac  Watts,  is  designed  as  a  guide  for  the 
attainment  of  useful  knowledge.  As  a  text-book  it  is  unparalleled ;  and  the  discipline 
it  affords  cannot  be  too  highly  esteemed  by  the  educator. 


MORALS. 

Peabody's  Moral  Philosophy. 

A  short  course,  by  the  Professor  of  Christian  Morals,  Harvard  University,  for  the 
Freshman  class  and  for  high  schools. 

Butler's  Analogy.     Hobart's  Analysis. 

Edited  by  Prof.  Charles  E.  West,  of  Brooklyn  Heights  Seminary.  228  pages.  16mo. 
Cloth. 

Alden's  Text-Book  of  Ethics. 

For  young  pupils.  To  aid  in  systematizing  the  ethical  teachings  of  the  Bible,  and 
point  out  the  coincidences  between  the  instructions  of  the  sacred  volume  and  the  sound 
conclusions  of  reason. 

Smith's  Elements  of  Moral  Philosophy. 

140  pages.  12mo.  Cloth.  By  Win.  Austin  Smith,  A.M.,  Ph.D.,  Professor  of  Moral 
Philosophy  in  the  Columbia  (Tenn.)  Athenseum. 

This  is  an  excellent  book  for  the  use  of  academies  and  schools.  It  is  prepared  to 
meet  the  wants  of  a  much  larger  public  than  has  heretofore  been  reached  by  works  of 
this  class.  The  subject  is  presented  in  clear  and  simple  language,  and  will  be  found 
adapted  to  the  comprehension  of  young  pupils,  at  a  time  when  they  particularly  need 
an  insight  into  the  laws  which  govern  the  moral  world. 

Janet's  Elements  of  Morals. 

By  Paul  Janet.     Translated  by  Mrs.  Prof.  Corson,  of  Cornell  University. 

The  Elements  of  Morals  is  one  of  a  series  of  works  chiefly  devoted  to  Ethics,  and 
treats  of  practical,  rather  than  theoretical  morality. 

Mr.  Janet  is  too  well  known  that  it  be  necessary  to  call  attention  to  his  excellence 
as  a  moral  writer,  and  it  will  be  sufficient  to  say  that  what  particularly  recommends 
the  Elements  of  Morals  to  educators  and  students  in  general  is  the  admirable  adap- 
tation of  the  book  to  college  and  school  purposes. 

Besides  the  systematic  and  scholarly  arrangement  of  its  parts,  it  contains  series  of 
examples  and  illustrations  —  anecdotic,  historical  —  gathered  with  rare  impartiality 
from  both  ancient  and  modern  writers,  and  which  impart  a  peculiar  life  and  interest  to 
the  subject. 

Another  featnra  of  the  work  is  its  sound  religious  basis.  Mr.  Janet  is  above  all 
a  religious  moralist 


THE  NATIONAL   SERIES  OF  STANDARD   SCHOOL-BOOKS. 


FRENCH. 

Worman's  First  French  Book. 

On  same  plan  as  the  German  and  Spanish.  The  scholar  reads  and  speaks  from  the 
first  hour  understandingly  and  accurately.  83  pages. 

Worman's  Second  French  Book. 

Continues  the  work  of  the  First  Book,  and  is  a  valuable  Elementary  French  Reader. 
96  pages. 

Worman's  Le  Questionnaire. 

Exercises  on  the  First  French  Book.     98  pages.     Cloth. 

Worman's  Grammaire  Frangaise. 

Written  in  simple  French,  but  based  on  English  analogy.  It  therefore  dwells  upon  the 
Essentials,  especially  those  which  point  out  the  variations  of  the  French  from  the 
student's  vernacular.  184  pp. 

Worman's  Teacher's  Hand-Book. 

Or  Key  to  the  Grammaire  Francaise. 

Worman's  French  Echo. 

This  is  not  a  mass  of  meaningless  and  parrot-like  phrases  thrown  together  for 
a  tourist's  use,  to  bewilder  him  when  in  the  presence  of  a  Frenchman. 

The  "  Echo  de  Paris  "  is  a  strictly  progressive  conversational  book,  beginning  with  sim- 
ple phrases  and  leading  by  frequent  repetition  to  a  mastery  of  the  idioms  and  of  the 
every-day  language  used  in  business,  on  travel,  at  a  hotel,  in  the  chit-chat  of 
society. 

It  presupposes  an  elementary  knowledge  of  the  language,  such  as  may  be  acquired 
from  the  First  French  Book  by  Professor  Worman,  and  furnishes  a  runniny  French 
text,  allowing  the  learner  of  course  to  find  the  meaning  of  the  words  (in  the  appended 
Vocabulary),  and  forcing  him,  by  the  absence  of  English  in  the  text,  to  think  in 
French.  ' 


CHER  MONSIEUR  WORMAN, — Vous  me 
demandez  mem  opinion  sur  votre  "  Echo  de 
Paris"  et  quel  usage  j'en  fais.  Je  ne 
saurais  mieux  vous  repondre  qu'en  repro- 
duisant  une  lettre  que  j'ecrivais  derniere- 
mcnt  a  un  collegue  qui  etait,  me  disait-il, 
"  bien  fatigue  d<j  ces  insipides  livres  de 
dialogues. " 

"  Vous  ne  connaissez  done  pas,"  lui 
disais-je,  "  '  1'Echo  de  Paris,'  edite  par  le 
Professor  Worman?  C'est  un  veritable 
tresor,  merveilleusement  adapte  au  devel- 
oppemeut  de  la  conversation  familiere  et 
pratique,  telle  qu'on  la  veut  aujourd'hui. 
Cet  excellent  livre  met  successivement  en 
scene,  d'une  maniere  vive  et  interessante, 


toutes  les  circonstances  possibles  de  la  vie 
ordinaire.  Voyez  1'imniense  avantage 
il  vous  transporte  en  France  ;  du  premier 
mot,  je  m'imagine,  et  mes  eleves  avec  moi, 
que  nous  sommes  a  Paris,  dans  la  rue,  sur 
Hne  place,  dans  une  gare,  dans  un  salon, 
dans  une  chambre,  voire  mfiine  a  la  cui- 
sine ;  je  parle  comme  avec  des  Frangais  ; 
les  eleves  ne  songent  pas  a  traduire  de 
Panglais  pour  me  repondre  ;  ils  pensent 
en  francjais  ;  ils  sont  Fran$ais  pour  le 
moment  par  les  yeux,  par  1'oreille,  par  la 
pensee  Quel  autre  livre  pourrait  produir* 
cette  illusion?  .  .  ." 

Votre  tout  afivoue', 

A-  DE  ROUGEMONT. 


Illustrated  Language  Primers. 

FRENCH  AND  ENGLISH.  GERMAN  AND  ENGLISH. 

SPANISH  AND  ENGLISH. 

The  names  of  common  objects  properly  illustrated  and  arranged  in  easy  lessons. 

Pujol's  Complete  French  Class-Book. 

Offers  in  one  volume,  methodically  arranged,  a  complete  French  course  —  usually 
embraced  in  series  of  from  five  to  twelve  books,  including  the  bulky  and  expensive 
lexicon.  Here  are  grammar,  conversation,  and  choice  literature,  selected  from  the 
best  French  authors.  Each  branch  is  thoroughly  handled  ;  and  the  student,  having 
diligently  completed  the  course  as  prescribed,  may  consider  himself,  without  further 
application,  au  fait  in  the  most  polite  and  elegant  language  of  modern  times. 

57 


THE  NATIONAL   SERIES  OF  STANDARD  SCHOOL-BOOKS. 

MODERN  LANGUAGES— Continued. 

Pujol's  French  Grammar,  Exercises,  Reader.     3  vols. 

These  volumes  contain  Part  I.,  Parts  II.  and  III.,  and  Part  IV.  of  the  Complete  Class- 
Book  respectively,  for  the  convenience  of  scholars  and  teachers.  The  Lexicon  is  bound 
with  each  part 

Maurice-Poitevin's  Grammaire  Franchise. 

American  schools  are  at  last  supplied  with  an  American  edition  of  this  famous  text- 
book. Many  of  our  best  institutions  have  for  years  been  procuring  it  from  abroad 
rather  than  forego  the  advantages  it  offers.  The  policy  of  putting  students  who  have 
acquired  some  proficiency  from  the  ordinary  text-books,  into  a  Grammar  written  in  the 
vernacular,  cannot  be  too  highly  commanded.  It  affords  an  opportunity  for  finish  and 
review  at  once,  while  embodying  abundant  practice  of  its  own  rules. 


SPANISH. 

Worman's  First  Spanish  Book. 

On  same  plan  as  Worman's  lirst  German  and  French  Books.  Teaches  by  direct  ap- 
peal to  illustrations,  and  by  contrast,  association,  and  natural  inference.  90  pp. 

These  little  books  work  marvels  in  the  school-room.  The  exercises  are  so  developed 
out  of  pictured  objects  and  actions,  and  are  so  well  graduated,  that  almost  Irom  the 
very  outset  they  go  alone.  A  beginner  would  have  little  use  for  a  dictionary  in  reading. 
The  words  are  so  introduced,  and  so  often  used,  that  the  meaning  is  kept  constantly 
before  the  mind,  without  the  intervention  of  a  translation. 

OTHER  SPANISH  BOOKS  TO  FOLLOW. 


ANCIENT    LANGUAGES. 


LATIN. 

Searing's  Virgil's  .flSneid,  Georgics,  and  Bucolics. 

1.  It  contains  the  first  six  books  of  the  .Eneid  and  the  entire  Bucolics  and  Georgics. 
2.  A  very  carefully  constructed  Dictionary.  3.  Sufficiently  copious  notes.  4.  Gram- 
matical references  to  four  leading  Grammars.  5.  Numerous  illustrations  of  the  highest 
order.  6.  A  superb  map  of  the  Mediterranean  and  adjacent  countries.  7.  Dr.  S.  H. 
Taylor's  "Questions  on  the  Aineid."  8.  A  Metrical  Index,  and  an  essay  on  the 
Poetical  Style.  9.  A  photographic  fac-simile  of  an  early  Latin  MS.  10.  The  text  is 
according  to  Jahn,  but  paragraphed  according  to  Ladewig.  11.  Superior  mechanical 
execution. 


"  My  attention  was  called  to  Searing's 
Virgil  by  the  fact  of  its  containing  a  vo- 
cabulary which  would  obviate  the  neces- 
sity of  procuring  a  lexicon.  But  use  in 
the  class-room  has  impressed  me  most 
favorably  with  the  accuracy  and  just  pro- 
portion of  its  notes,  and  the  general  ex- 
cellence of  its  grammatical  suggestions. 


paper,  its  typography,  and  its  engravings, 
is  highly  commendable,  and  the  jac-simile 
manuscript  is  a  valuable  feature.  I  take 
great  pleasure  in  commending  the  bonk  to 
all  who  do  not  wish  a  complete  edition  of 
Virgil.  It  suits  our  short  school  courses 
admirably."  HENRY  L.  BOLTWOOD,  Mas~ 
ter  Princeton  High  School,  III. 


The  general  character  of  the  book,  in  its 

Johnson's  Persius. 

The  Satires  of  Aulus  Persius  Flaccus,  edited,  with  English  notes,  principally  from 
Conington.  By  Henry  Clark  Johnson,  A.  M. ,  LL.B.,  Professor  of  Latin  in  the  Lehigb 
University. 

58 


THE  NATIONAL   SERIES  OF  STANDARD  SCHOOL-BOOKS. 

SCHOOL   MUSIC. 

Ryan's   Vocalist. 

A  new  singing  book  for  Graded  Schools,  Seminaries  and  social  assemblies.  232  pages, 
long  8vo,  cloth. 

The  National  School  Singer. 

Bright,  new  music  for  the  day  school,  embracing  Song  Lessons,  Exercise  Songs,  Songs 
of  Study,  Order,  Promptness,  and  Obedience,  of  Industry  and  Nature,  Patriotic  and 
Temperance  Songs,  Opening  and  Closing  Songs  ;  in  fact,  everything  needed  in  the 
school-room.  By  an  eminent  musician  and  composer. 

Jepson's  Music  Readers.     3  vols. 

These  are  not  books  from  which  children  simply  learn  songs,  parrot-like,  but  teach 
the  subject  progressively,  the  scholar  learning  to  read  music  by  methods  similar  to 
those  employed  in  teaching  him  to  read  printed  language.  Any  teacher,  however  igno- 
rant of  music,  provided  he  can,  upon  trial,  simply  sound  the  scale,  may  teach  it  without 
assistance,  and  will  end  by  being  a  good  singer  himself.  The  "  Elementary  Music 
Reader,"  or  first  volume,  fully  develops  the  system.  The  two  companion  volumes  carry 
the  same  method  into  the  higher  grades,  but  their  use  is  not  essential. 

The  First  Reader  is  also  published  in  three  parts,  at  thirty  cents  each,  for  those  who 
prefer  them  in  that  form. 

Nash  and  Bristow's  Cantara. 

The  first  volume  is  a  complete  musical  text-book  for  schools  of  every  grade.  No.  2  is 
a  choice  selection  of  solos  and  part  songs.  The  authors  are  Directors  of  Music 
in  the  public  schools  of  New  York  City,  in  which  these  books  are  the  standard  of 
instruction. 

The  Polytechnic. 

Collection  of  Part  Songs  for  High  and  Normal  Schools  and  Clubs.  This  work  con- 
tains a  quantity  of  exceedingly  valuable  material,  heretofore  accessible  only  in  sheet 
form  or  scattered  in  mumerous  and  costly  works.  The  collection  of  "  College  Songs  " 
is  a  very  attractive  feature. 

Curtis's  Little  Singer:  —  School  Vocalist.  —  Kings- 
ley's  School-Room  Choir.  —  Young  Ladies' 
Harp.  —  Hager's  Echo  (A  Cantata). 


SCHOOL  DEVOTIONAL  EXERCISE. 

Brooks's  School  Manual  of   Devotion. 

This  volume  contains  daily  devotional  exercises,  consisting  of  a  hymn,  selections  of 
Scripture  for  alternate  reading  by  teacher  and  pupils,  and  a  prayer.  Its  value  for  open- 
ing and  closing  school  is  apparent. 

Brooks's  School  Harmonist. 

Contains  appropriate  tunes  for  each  hymn  in  the  "  Manual  of  Devotion  "  described 
above. 

Bartley's  Songs  for  the  School. 

A  selection  of  appropriate,  hymns  of  an  unsectarian  character,  carefully  classified 
and  set  to  popular  and  "  singable  "  tunes,  for  opening  and  closing  exercises.  The  Secu- 
lar Department  is  full  of  bright  and  well-selected  music. 

61 


THE  NATIONAL    SERIES   OF  STANDARD   SCHOOL-BOOKS. 
TEACHERS'  AIDS  AND  SCHOOL  REQUISITES. 

CHARTS  AND   MAPS. 

Baade's  Reading  Case. 

This  remarkable  piece  of  school-room  furniture  is  a  receptacle  containing  a  number 
of  primary  cards.  By  an  arrangement  of  slides  ou  the  front,  one  sentence  at,  a  time  is 
shown  to  the  class.  Twenty-eight  thousand  transpositions  may  be  made,  affording  a 
variety  of  progressive  exercises  which  no  other  piece  of  apparatus  offers.  One  of  its 
best  features  is,  that  it  is  so  exceedingly  simple  as  not  to  get  out  of  order,  while  it  may 
be  operated  with  one  finger. 

Clark's  Grammatical  Chart. 

Exhibits  the  whole  science  of  language  in  one  comprehensive  diagram. 

Davies's  Mathematical  Chart. 

Elementary  mathematics  clearly  taught  to  a  full  class  at  a  glance. 

De    Rupert's    Philological    and    Historical    Chart. 

This  very  comprehensive  chart  shows  the  birth,  development,  and  progress  of  the 
literatures  of  the  world  ;  their  importance,  their  influence  on  each  other,  and  the  cen- 
tury in  which  such  influence  was  experienced  ;  with  a  list  for  each  country  of  standard 
authors  and  their  best  works.  Illustrating  also  the  division  of  languages  into  classes, 
families,  and  groups.  Giving  date  of  settlement,  discovery,  or  conquest  of  all  countries, 
with  their  government,  religion,  area,  population,  and  the  percentage  of  enrolment  for 
1872,  in  the  primary  schools  of  Europe  and  America. 

Eastman's  Chirographic  Chart.      Family  Record. 
Giffins's  Number  Chart. 

Teaches  addition,  subtraction,  multiplication,  and  division.    Size,  23x31  inches. 

Marcy's  Eureka  Tablet. 

A  new  system  for  the  alphabet,  by  which  it  may  be  taught  without  fail  in  nine  lessons. 

McKenzie's  Elocutionary  Chart. 
Monteith's  Pictorial  Chart  of  Geography. 

A  crayon  picture  illustrating  al!  the  divisions  of  the  earth's  surface  commonly 
taught  in  geography. 


WM.  L.  DICKINSON,   Superintendent  of 

Schools,  Jersey  C'ty,  says. 
"  It  is  an  admirable  amplification  of  the 


in  all  good  geographies.  I  think  the 
chart  would  be  a  great  help  in  any  pri- 
mary department." 


system  of  pictorial   illustration  adopted 

Monteith's  Reference  Maps.     School  and  Grand  Series. 

Names  all  laid  down  in  small  type  so  that  to  the  pupil  at  a  short  distance  they  are 
outline  maps,  while  they  serve  as  tlieir  own  key  to  the  teacher. 

Page's  Normal  Chart. 

The  whole  science  of  elementary  sounds  tabulated. 

Scofield's  School  Tablets. 

On  five  cards,  exhibiting  ten  surfaces.  These  tablets  teach  orthography,  reading, 
object-lessons,  color,  form,  &c. 

Watson's  Phonetic  Tablets. 

Four  cards  and  eight  surfaces  ;  teaching  pronunciation  and  elocution  phonetically. 
For  class  exercises. 

Whitcomb's  Historical  Chart. 

A  student's  topical  historical  chart,  from  the  creation  to  the  present  time,  including 
results  of  the  latest  chronological  research.  Arranged  with  spaces  for  summary,  that 
pupils  may  prepare  and  review  their  own  chart  in  connection  with  any  text-book. 

Willard's  Chronographers. 

Historical.  Four  numbers  :  Ancient  chronographer,  English  chronograpber,  Ameri- 
can chronographer,  temple  of  time  (general).  Dates  and  events  represented  to  the  eye. 

62 


THE  NATIONAL   SERIES  OF  STANDARD  SCHOOL-BOOKS. 


CHARTS,  &c.  —  Continued. 

Popular  Folding  Reading  Charts. 

In  two  parts.  Price  $5.00  each.  These  fifty-three  charts  are  the  outgrowth  of  prac- 
tical reading  lessons,  all  of  which  have  been  tried  witli  classes  of  little  children,  first 
as  black-board  lessons,  and  afterward  as  printed  manuscripts.  By  this  method  all  the 
lessons  were  adapted  to  the  capacity  of  the  children.  The  words  have  been  carefully 
selected  and  graded  from  the  child's  own  spoken  vocabulary. 

PART    I. 

The  new  words  of  the  first  part  are  taught 
by  the  word  and  sentence  method,  the  object- 
words  being  illustrated  by  engravings. 

All  the  lessons  sparkle  with  real  childlike 
expressions.  The  language  is  the  language 
of  childhood,  and  thus  to  the  pupil  becomes 
doubly  interesting  while  at  the  same  time 
progressive. 

The  Clock  Face,  with  Movable  Hands,  is 
an  important  and  attractive  feature.  The  au- 
thors know  from  experience  that  very  happy 
results  can  be  had  by  its  use.  Teaching  chil- 
dren to  tell  the  time  has  always  been  expected 
of  the  teacher,  though  seldom,  if  ever,  has  an 
opportunity  been  afforded  him  to  do  so. 

All  the  letters  of  the  alphabet  are  taught  by 
a  series  of  writing  lessons  in  the  order  uf 
their  development,  and  are  finally  grouped  to- 
gether in  a  script  alphabet. 


UNIQUE 

READING 

CHART 


Kfolded) 


PART  II 

takes  up  the  development  of  the  elementary 
sounds  of  the  langu;  ge,  from  the  words  already 
learned  in  Part  I.,  ir,  such  a  way  as  to  enable 
the  child  to  see  for  himself  how  words  are  made, 
and  giving  the  k«y  by  which  he  can  make  out 
for  himself  new  words. 

A  series  of  language  lessons  is  the  feature 
of  this  part,  by  which  children  are  gradually 
taught  the  use  of  words  by  composing  brief 
sentences  nwl  original  stories. 

The  Color  Chart  is  the  most  unique  feature 
ever  offered  to  the  public,  enabling  the  teacher 
to  teach  the  primary  and  secondary  colors  from 
nature. 

Many  review  lessons  are  Riven  in  order  that 
the  children  may  learn  to  rear!  by  reading. 

No  easel  or  framework  of  any  kind  is  re- 
quired with  the  chart.  The  publishers  have 
secured  the  exclusive  ritrht  to  use  Shepard's 
Patent  Chart  Binding,  the  use  of  which 
ghes  it  a  decided  advantage  over  any  other 
reading  chart  yet  made.  It  is  in  this  respect 
unapproachable. 


G3 


little  >HRgirl 
A  little  girl. 


Here  is  a  girl. 
Here  is  alittle  girl. 


THE  NATIONAL   SERIES  OF  STANDARD   SCHOOL-BOOKS. 


COPY-BOOKS,    &c. 

Barnes's  New  National  System  of  Penmanship. 

This  new  series  of  Copy-books,  iii  six  numbers,  is  based  upon  many  years'  experience. 
The  publishers  think  these  books  are  the  best  ever  made  in  this  country,  for  the  following 
reasons  :  — 

1.  They  contain  a.  thoroughly  Practical  System  of  Penmanship,  which,  if  once  well 
learned  in  school,  will  not  prove  too  difficult  of  execution  for  business  purposes  or  private 
correspondence. 

2.  They  have  been  prepared  in  the  most  careful  manner,  without  regard  to  expense 
by  experts  in  the  business ;  and  the  copies  are  infinitely  superior  to  all  others  in  the 
mar.cet,  not  only  in  beauty  and  grace  of  style,  but  also  in  accuracy  of  outline  and 
proportion. 

3.  Pupils  who  use  these  books  as  directed  will  write  in  a  free,  graceful,  rapid  man 
ner,  and  not  in  the  slow,  cramped,  and  crabbed  style  so  common  in  many  schools. 

4.  The  classification  of  capitals  is  wonderfully  simplified.     Eleven  letters  are  formed 
on  one  general  plan  ;  ten  on  another,  and  the  rest  on  a  third.     The  number  of  elements 
is  reduced  to  h've.     Other  systems  have  from  seven  to  thirteen. 

5.  The  gradation  is  perfectly  simple.    Only  familiar  words,  and  those  easy  of  forma- 
tion, are  used,  and  not  such  unusual  enigmatical  words  as  "zeugma,"  "  unjue.sne  " 
"  xylus,"  "  tenafly,"  ''quinque,"  "  minetic,"  "  xuthus,"  and  the  like,  that  have  long 
been  the  bane  of  both  teachers  and  pupils. 

6.  No  time  has  been  lost  by  placing  before  the  pupil  disconnected  words,  unmean- 
ing phrases,  and  stale  aphorisms  ;  but  the  complete  sentence  has  been  used  early  in  the 
series,  that  the  pupil,  while  writing,  might  be  expressing  thoughts,  rather  than  simply 
copying  abstract  words. 

7.  The  business  forms  are  elaborately  engraved  on  steel  and  printed  on  patent  safety- 
tint  paper.     They  are  exactly  like  the  checks,  notes,  drafts,  receipts,  etc.,  used  in 
business,  and  the  learning  how  to  fill  them  out  will  serve  as  an  admirable  introduction 
to  the  counting-room. 

8.  The  whole  series  for  ungraded  schools  is  comprised  in  six  books  ;  but  for  the 
benefit  of  the  large,  graded  schools  in  both  city  and  country,  there  are  six  additional 
books,  of  smaller  size,  to  meet  the  demands  of  a  still  closer  gradation. 

Ward's   Letter-Writing  and    Business   Forms. 

For  Schools  and  Academies.  In  Four  Numbers.  No.  1,  Letters  and  Bills.  No.  2, 
Letters,  Receipts,  Accounts,  etc.  No.  3,  Letters,  Notes,  Drafts,  etc.  No.  4,  General 
Practice.  48  pages  each.  Price  15  cents  each. 

Intended  to  supply  more  practical  work  in  the  school-room.  Letter-writing,  Bills, 
Receipts,  Accounts,  Checks,  Notes,  and  all  Commercial  forms  are  given  for  practice. 

Beers's   System   of  Progressive   Penmanship. 

This  "round  hand  "  system  of  Penmanship,  in  twelve  numbers,  commends  itself  by 
its  simplicity  and  thoroughness.  The  first  four  numbers  are  primary  books.  Nos.  5  to 
7,  advanced  books  for  boys.  Nos.  8  to  10,  advanced  books  tor  girls.  Nos.  11  and  12, 
ornamental  penmanship.  These  books  are  printed  from  steel  plates  (engraved  by 
McLees),  and  are  unexcelled  in  mechanical  execution. 

Beers's   Slated   Copy   Slips. 

Slate  exercises,  familiarizing  beginners  with  the  form  of  the  letters,  the  motions  of 
the  hand  and  arm,  etc. ,  etc.  These  copy  slips,  32  in  number,  supply  all  the  copies  found 
in  a  complete  series  of  writing-books,  at  a  trifling  cost. 

Fulton  &  Eastman's  Chirographic  Charts 

To  embellish  the  school-room  walls,  and  furnish  class  exercise  in  the  elements  of 
Penmanship. 

Payson's  Copy-Book  Cover. 

Protects  every  p;if;e  except  the  one  in  use,  and  furnishes  "  lines  "  with  proper  slope 
*»r  the  penman,  under.  Patented. 

65 


THE:  NATIONAL  SERIES  OF  STANDARD  MISCELLANY. 

LIBRARY  AND  MISCELLANEOUS 
PUBLICATIONS. 


TEACHERS'    WORKING    LIBRARY. 
Object  Lessons.     Welch. 

This  is  a  complete  exposition  of  the  popular  modern  system  of  "object-teaching," 
for  teachers  of  primary  classes. 

Theory  and  Practice  of  Teaching.     Page. 

This  volume  has,  without  doubt,  been  read  by  two  hundred  thousand  teachers,  and 
its  popularity  remains  undiminished,  large  editions  being  exhausted  yearly.  It  was 
the  pioneer,  as  it  is  now  the  patriarch,  of  professional  works  for  teachers. 

The  Graded  School.     Wells. 

The  proper  way  to  organize  graded  schools  is  here  illustrated.  The  author  has  availed 
himself  of  the  best  elements  of  the  several  systems  prevalent  in  Boston,  New  York, 
Philadelphia,  Cincinnati,  St.  Louis,  and  other  cities. 

The  Normal.     Holbrook. 

Carries  a  working  school  on  its  visit  to  teachers,  showing  the  most  approved  methods 
of  teaching  all  the  common  branches,  including  the  technicalities,  explanations,  demon- 
strations, and  definitions  introductory  and  peculiar  to  each  branch. 

School  Management.     Holbrook. 

Treating  of  the  teacher's  qualifications  ;  how  to  overcome  difficulties  in  self  and 
others  ;  organization  ;  discipline  ;  methods  of  inciting  diligence  and  order  ;  strategy 
in  management ;  object-teaching. 

The  Teachers'  Institute.     Fowle. 

This  is  a  volume  of  suggestions  inspired  by  the  author's  experience  at  institutes,  in 
the  instruction  of  young  teachers.  A  thousand  points  of  interest  to  this  class  are  most 
satisfactorily  dealt  with. 

Schools  and  Schoolmasters.     Dickens. 

Appropriate  selections  from  the  writings  of  the  great  novelist. 

The  Metric  System.    Davies. 

Considered  with  reference  to  its  general  introduction,  and  embracing  the  views  of 
John  Quiney  Adams  and  Sir  John  Herschel. 

The  Student ;  The  Educator.     Phelps.     2  vols. 
The  Discipline  of  Life.     Phelps. 

The  authoress  of  these  works  is  one  of  the  most  distinguished  writers  on  education, 
and  they  cannot  fail  to  prove  a  valuable  addition  to  the  School  and  Teachers'  Libraries, 
being  in  a  high  degree  both  interesting  and  instructive. 

Law  of  Public  Schools.     Burke. 

By  Finley  Burke,  Counsellor-at-Law.  A  new  volume  in  "  Barnes's  Teachers'  Library 
Series."  12mo,  cloth. 


"Mr.  Burke  has  given  us  the  latest 
expositions  of  the  law  on  this  highly  im- 
portant subject.  I  shall  cordially  com- 
mend his  treatise."  —  THEODORE  DWIGHT, 
LL.D. 

From  the  HON.  JOSEPH  M.  BECK,   Judge  of 
Supreme  Court,  Iowa. 

"  I  have  examined  with  considerable 
Wire  the  manuscript  of  '  A  Treatise  on  the 


Law  of  Public  Schools. '  by  Finley  Burke, 
Esq.,  of  Council  Bluffs.  In  my  opinion, 
the  work  will  be  of  great  value  to  school 
teachers  and  school  officers,  and  to  law- 
yers. The  subjects  treated  of  are  thought- 
fully considered  and  thoroughly  examined, 
and  correctly  and  systematically  arranged. 
The  style  is  perspicuous.  The  legal  doc- 
trines of  the  work,  so  far  as  I  have  been 


66 


THE   NATIONAL    SERIES    OF   STANDARD    MISCELLANY. 


MISCELLANEOUS    PUBLICATIONS  —  Continued. 


able  to  consider  them,  are  sound.  I  have 
examined  quite  a  number  of  the  authori- 
ties cited ;  they  sustain  the  rules  an- 
nounced in  the  text.  Mr.  Burke  is  an  able 
and  industrious  member  of  the  bar  of  the 
Supreme  Court  of  this  State,  and  has  a 
high  standing  in  the  profession  of  the 
law." 

"  I  fully  concur  in  the  opinion  of  Judge 
Beck,  above  expressed." — JOHN  F.  DIL- 
LON. New  York,  May,  1880. 

Sioux  CITY,  IOWA,  May,  1880. 
I  have  examined  the  manuscript  of 
Finley  Burke,  Esq. ,  and  find  a  full  citation 
of  all  the  cases  and  decisions  pertaining  to 
the  school  law,  occurring  in  the  courts  of 
the  United  States.  This  volume  contains 


valuable  and  important  information  con- 
cerning school  law,  which  has  never  before 
been  accessible  to  either  teacher  or  school 
officer.  A.  ARMSTRONG, 

Suft.  Schools,  Sioux  City,  fotca. 

DES  MOINES,  May  15,  1880. 
The  examination  of  "  A  Treatise  on  the 
Law  of  Public  Schools,"  prepared  by  Fin- 
ley  Burke,   Esq. ,  of   Council  Blufl's,  has 
fiven  me  much  pleasure.     So  far  as  I 
now,  there  is  no  work  of  similar  charac- 
ter now  in  existence.    I  think  such  a  work 
will  be    exceedingly  useful   to    lawyers, 
school  officers,  and  teachers,  and  I  hope 
that  it  may  find  its  way  into  their  hands. 
G.  W.  VON  COELLV, 

Supt.  Public  Inst.  for  Iowa. 


Teachers'  Handbook.     Phelps. 

By  William  F.  Phelps,  Principal  of  Minnesota  State  Normal  School.  Embracing  the 
objects,  history,  organization,  and  management  of  teachers'  institutes,  followed  by 
methods  of  teaching,  in  detail,  for  all  the  fundamental  branches.  Every  young  teacher, 
•very  practical  teacher,  every  experienced  teacher  even,  needs  this  book. 

This  is  the  key-note  of  the  present  excel- 
lent volume.  In  view  of  the  supreme 
importance  of  the  teacher's  calling,  Mr. 

prepare  the  child  for  the  discipline  of  life.        Phelps  has  presented  an  elaborate  system 
Th»   country  schoolmaster,  accordingly,        of  instruction  in  the  elements  of  learning, 


From  the  New  Fork  Tribune. 


"The  discipline  of  the  school  should 
prepare  the  child  for  the  discipline  of  life. 
Th»  country  schoolmaster,  accordingly, 
holds  a  position  of  vital  interest  to  the 
destiny  of  the  republic,  and  should  neg- 
lect no  means  for  the  wise  and  efficient 
discharge  of  his  significant  functions. 


with  a  complete  detail  of  methods  and 
processes,  illustrated  with  an  abundance 
of  practical  examples  and  enforced  by 
judicious  councils." 


Topical  Course  of  Study.     Stone. 

This  volume  is  a  compilation  from  the  courses  of  study  of  our  most  successful  public 
schools,  and  the  best  thought  of  leading  educators.  The  pupil  is  enabled  to  make  full 
use  of  any  and  all  text-books  bearing  on  the  given  topics,  and  is  incited  to  use  all  other 
information  within  his  reach. 

American  Education.     Mansfield. 

A  treatise  on  the  principles  and  elements  of  education,  as  practised  in  this  country, 
With  ideas  towards  distinctive  republican  and  Christian  education. 

American  Institutions.     De  Tocqueville. 

A  valuable  index  to  the  genius  of  our  Government. 

Universal  Education^     Mayhew. 

The  subject  is  approached  with  the  clear,  keen  perception  of  one  who  has  observed 
its  necessity,  and  realized  its  feasibility  and  expediency  alike.  The  redeeming  and 
elevating  power  of  improved  common  schools  constitutes  the  inspiration  of  the  volume. 

Oral  Training  Lessons.     Barnard. 

The  object  of  this  very  useful  work  is  to  furnish  material  for  instructors  to  impart 
orally  to  their  classes,  in  branches  not  usually  taught  in  common  schools,  embracing  a.1' 
departments  of  natural  science  and  much  general  knowledge. 

Lectures  on  Natural  History.     Chadbourne. 

Affording  many  themes  for  oral  instruction  in  this  interesting  scisnc*,  especially  in 
schools  where  it  is  not  pursued  as  a  class  exercise. 

67 


X 

THE  NATIONAL   SERIES   OF  STANDARD   MISCELLANY. 

MISCELLANEOUS   PUBLICATIONS  —  Continued. 

Outlines  of  Mathematical  Science.     Davies. 

A  manual  suggesting  the  best  methods  of  presenting  mathematical  instruction  on  the 
part  of  the  teacher,  with  that  comprehensive  view  of  the  whole  which  is  necessary  to 
the  intelligent  treatment  of  a  part,  iu  science. 

Nature  and  Utility  of  Mathematics.     Davies. 

An  elaborate  and  lucid  exposition  of  the  principles  which  lie  at  the  foundation  of 
pure  mathematics,  with  a  highly  ingenious  application  of  their  results  to  the  develop- 
ment of  the  essential  idea  of  the  different  branches  of  the  science. 

Mathematical  Dictionary.     Davies  and  Peck. 

This  cyclopaedia  of  mathematical  science  defines,  with  completeness,  precision,  and 
accuracy,  every  technical  term  ;  thus  constituting  a  popular  treatise  on  each  branch, 
and  a  general  view  of  the  whole  subject. 

The  Popular  Educator.     Barnes. 

In  seven  volumes,  containing  interesting  and  profitable  educational  miscellany. 

Liberal  Education  of  Women.     Orton. 

Treats  of  "  the  demand  and  the  method  ;  "  being  a  compilation  of  the  best  and  most 
advanced  thought  on  this  subject,  by  the  leading  writers  and  educators  in  England  and 
America.  Edited  by  a  professor  in  Vassar  College. 

Education  Abroad.     Northrop. 

A  thorough  discussion  of  the  advantages  and  disadvantages  of  sending  American 
children  to  Europe  to  be  educated  ;  also,  papers  on  legal  prevention  of  illiteracy,  study, 
and  health,  labor  as  an  educator,  and  other  kindred  subjects. 

The  Teacher  and  the  Parent.     Northend. 

A  treatise  upon  common-school  education,  designed  to  lead  teachers  to  view  their 
calling  in  its  true  light,  and  to  stimulate  them  to  fidelity. 

The  Teachers'  Assistant.     Northend. 

A  natural  continuation  of  the  author's  previous  work,  more  directly  calculated  for 
daily  use  iu  the  administration  of  school  discipline  and  instruction. 

School  Government.     Jewell. 

Full  of  advanced  ideas  on  the  subject  which  its  title  indicates.  The  criticisms  upon 
current  theories  of  punishment  and  schemes  of  administration  have  excited  general 
attention  and  comment. 

Grammatical  Diagrams.     Jewell. 

The  diagram  system  of  teaching  grammar  explained,  defended,  and  improved.  The 
curious  in  literature,  the  searcher  for  truth,  those  interested  in  new  inventions,  as  well 
as  the  disciples  of  Professor  Clark,  who  would  see  their  favorite  theory  fairly  treated, 
all  want  this  book.  There  are  many  who  would  like  to  be  made  familiar  with  this 
system  before  risking  its  use  in  a  class.  The  opportunity  is  here  afforded. 

The  Complete  Examiner.     Stone. 

Consists  of  a  series  of  questions  on  every  English  branch  of  school  and  academic 
instruction,  with  reference  to  a  given  page  or  article  of  leading  text-books  where  the 
answer  may  be  found  in  full.  Prepared  to  aid  teachers  in  securing  certificates,  pupils 
in  preparing  for  promotion,  and  teachers  in  selecting  review  questions. 

How  Not  to  Teach.     Griffin. 

This  book  meets  a  want  universally  felt  among  young  teachers  who  have  their  expe- 
rience in  teaching  to  learn.  It  undertakes  to  point  out  the  many  natural  mistakes  into 
which  teachers,  unconsciously  or  otherwise,  fall,  and  warns  the  reader  against  dangers 
that  beset  the  path  of  every  conscientious  teacher.  It  tells  tlie  reader,  also,  the  proper 
and  acceptable  way  to  teach,  illustrating  the  author's  ideas  by  some  practice-lessons 
in  arithmetic  (after  Griibe).  gg 


THE  NATIONAL    SERIES    OF  STANDARD   MISCELLANY, 

MISCELLANEOUS  PUBLICATIONS  —  C<mti,iue<L 

School  Amusements.     Root. 

To  assist  teachers  in  making  the  school  interesting,  with  hints  upon  the  manage- 
ment of- the  school-room.  Rules  for  military  and  gymnastic  exercises  are  included. 
Illustrated  by  diagrams. 

Institute  Lectures.     Bates. 

These  lectures,  originally  delivered  before  institutes,  are  based  upon  various  topics  in 
the  departments. of  mental  and  moral  culture.  The  volume  is  calculated  to  prepare 
the  will,  awakeii  the  inquiry,  and  stimulate  the  thought  of  the  zealous  teacher. 

Method  of  Teachers'  Institutes.     Bates. 

Sets  forth  the  best  method  of  conducting  institutes,  with  a  detailed  account  of  the 
object,  organization,  plan  of  instruction,  and  true  theory  of  education  on  which  such 
instruction  should  be  based. 

History  and  Progress  of  Education. 

The  systems  of  education  prevailing  in  all  nations  and  ages,  the  gradual  advance  to 
the  present  time,  and  the  bearing  of  the  past  upon  the  present,  in  this  regard,  are 
worthy  of  the  careful  investigation  of  all  concerned  in  education. 

Higher  Education.     Atlas  Series. 

A  collection  of  valuable  essays.  CONTENTS.  International  Communication  by  Lan- 
guage, by  Philip  Gilbert  Hamerton  ;  Reform  in  Higher  Education  ;  Upper  Schools,  by 
President  James  McCosh  ;  Study  of  Greek  and  Latin  Classics,  by  Prof.  Charles 
Elliott  ;  The  University  System  in  Italy,  by  Prof.  Angelo  de  Gubernatis,  of  the 
University  of  Florence ;  Universal  Education,  by  Ray  Palmer ;  Industrial  Art  Educa- 
tion, by  Eaton  8.  Drone. 


LIBRARY    OF    LITERATURE. 

Milton's  Paradise  Lost.     (Boyd's  Illustrated  Edition.) 
Young's  Night  Thoughts.  do. 

Cowper's  Task,  Table  Talk,  &c.        do. 
Thomson's  Seasons.  do. 

Pollok's  Course  of  Time.  do. 

These  works,  models  of  the  best  and  purest  literature,  are  beautifully  illustrated,  and 
notes  explain  all  doubtful  meanings. 

Lord  Bacon's  Essays.     (Boyd's  Edition.) 

Another  grand  English  classic,  affording  the  highest  example  of  purity  in  language 
and  style. 

The  Iliad  of  Homer.     (Translated  by  Pope.) 

Those  who  are  unable  to  read  this  greatest  of  ancient  writers  in  the  original  should 
not  fail  to  avail  themselves  of  this  standard  metrical  version. 

Pope's  Essay  on  Man. 

This  is  a  model  of  pure  classical  English,  which  should  be  read,  also,  by  every  teacher 
and  scholar  for  the  sound  thought  it  contains. 

Improvement  of  the  Mind.     Isaac  Watts. 

No  mental  philosophy  was  ever  written  which  is  so  comprehensive  and  practically 
useful  to  the  unlearned  as  well  as  learned  reader  as  this  well-known  book  of  Watts. 

Milton's  Political  Works.     Cleveland. 

This  is  the  very  best  edition  of  the  great  poet.  It  includes  a  life  of  the  author, 
notes,  dissertations  on  each  poem,  a  faultless  text,  and  is  the  only  edition  of  Miltou 
with  a  complete  verbal  index. 

6? 


THE  NATIONAL    SERIES    OF  STANDARD   MISCELLANY, 

MISCELLANEOUS  PUBLICATIONS  —  Continued. 

Compendium  of  English  Literature.     Cleveland. 
English  Literature  of  XlXth  Century.     Cleveland. 
Compendium  of  American  Literature.     Cleveland. 

Nearly  one  hundred  and  fifty  thousand  volumes  of  Professor  Cleveland's  inimitable 
compendiums  have  been  sold.  Taken  together  they  present  a  complete  view  of  litera- 
ture. To  the  man  who  can  afford  but  a  few  books  these  will  supply  the  place  of  an 
extensive  library.  From  commendations  of  the  very  highest  authorities  the  following 
extracts  will  give  some  idea  of  the  enthusiasm  with  which  the  works  are  regarded  by 
scholars :  — 

"  With  the  Bible  and  your  volumes  one  might  leave  libraries  without  very  painful 
regret "  "  The  work  cannot  be  found  from  which  in  the  same  limits  so  much  interesting 
and  valuable  information  may  be  obtained."  "  Good  taste,  fine  scholarship,  familiar 
acquaintance  with  literature,  unwearied  industry,  tact  acquired  by  practice,  an  interest 
in  the  culture  of  the  young,  and  regard  for  truth,  purity,  philanthropy,  and  religion 
are  united  in  Mr.  Cleveland."  "  A  judgment  clear  and  impartial,  a  taste  at  once  deli- 
cate and  severe."  "The  biographies  are  just  and  discriminating."  "An  admirable 
bird's-eye  view."  "Acquaints  the  reader  with  the  characteristic  method,  tone,  and 
quality  of  each  writer."  "  Succinct,  carefully  written,  and  wonderfully  comprehensive 
in  detail,"  &c.,  &c. 


THE  TEACHER'S  READING  CIRCLE. 

"  No  movement  of  modern  times,  rapid  and  startling  as  have  been  the  changes  in 
school  methods,  has  ever  made  such  simple  and  economical  provisions  for  self-improve- 
ment among  teachers,  or  promises  such  wide  usefulness."  —  The  Educational  Weekly. 

"  A  better  indication  of  progress  even  than  the  improvement  and  increasing  number 
of  educational  journals,  is  the  formation  of  Teachers'  Reading  Circles.  More  may  be 
confidently  expected  from  these  associations  than  from  any  other  educational  movement 
ever  started  in  this  country."  —  The  Practical  Teacher. 

Among  the  leading  publications  selected  for  the  Teachers'  Reading  Circles  are  the 
following  :  — 

Barnes's  Brief  General  History  of  the  World. 

From  H.  M.  SKINNER,  Secy  Indiana  Reading  Circle  Hoard:  "  It  would  not  be  assert- 
ing too  much  to  say  that  if  an  author  thoroughly  competent  had  undertaken  the  prep- 
aration of  a  book  expressly  for  the  Reading  Circle,  —  a  book  intended  to  impart  general 
information  and  to  encourage  a  taste  for  reading,  —  a  work  better  adapted  to  the  Read- 
ing Circle  needs  than  Barnes's  General  History  would  hardly  have  been  possible." 

Page's  Theory  and  Practice  of  Teaching.    (New  Ed.) 

This  volume  has  without  doubt  been  read  by  several  hundred  thousand  teachers, 
and  its  popularity  remains  undiminished  —  large  editions  being  exhausted  yearly.  It 
was  the  pioneer,  as  it  is  now  the  patriarch,  of  professional  works  for  teachers. 

Watts's  Improvement  of  the  Mind.   (New  Edition.) 

The  ablest  production  of  one  of  the  most  eminent  writers  of  the  English  language. 
The  amount  of  practical  wisdom  contained  within  its  two  hundred  pages  has  challenged 
the  admiration  of  the  wisest  of  the  two  hemispheres  for  more  than  a  century.  This 
book  should  be  carefully  read  and  digested  by  every  teacher  and  advanced  student 

Hygiene  for  Young  People. 
Steele's  Hygienic  Physiology. 

These  books  are  of  unsurpassed  excellence.  The  text  of  each  is  brought  fully  up  to 
the  level  of  the  New  Physiological  views,  and  the  subjects  are  treated  with  special  refer- 
ence "  to  the  effects  of  alcoholic  drinks,  stimulants,  and  narcotics  upon  the  human 
system."  They  are  essential  to  every  well-regulated  teacher's  library. 

70 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 

Los  Angeles 
This  book  is  DUE  on  the  last  date  stamped  below. 


SUBJECT  TO  FINE  IF 

EDUCATIO 
JW»«    864 

APR  4     1966 

APR  10  1971 

"ECE/VED 

APR  9     ,97, 


SEP  13  1971 
RECEIVED 
SEP1     197 

EDU./PSYCH. 
UBRARY 

Form  L9-25m-3,'61(B8165b4)444 


RECEIVED 

AUG271973 

EDU.IPSYCH. 


4AN   91974 

RECEIVED 

JAN  08  1974 


UBWUtt 


QL  JUN  2  9  U81 


RECEIVED 

MAY  20 '81 -1PM 

ED/PSYCH  LIB. 


UCLA-ED/PSYCH  Library 

LBl169H12p 


L  005  602  654  5 


m  lil 


